Numerical properties of 1000101

June 30, 2024

Show numerical properties of 1000101

We start by listing out divisors for 1000101

Divisor	Divisor Math
1	1000101 ÷ 1 = 1000101
3	1000101 ÷ 3 = 333367
333367	1000101 ÷ 333367 = 3

Positive or Negative Number Test:

Positive Numbers > 0

Since 1000101 ≥ 0 and it is an integer
1000101 is a positive number

Whole Number Test:

Positive numbers including 0
with no decimal or fractions

Since 1000101 ≥ 0 and it is an integer
1000101 is a whole number

Prime or Composite Test:

Since 1000101 has divisors other than 1 and itself
it is a composite number

Perfect/Deficient/Abundant Test:

Calculate divisor sum D

If D = N, then it's perfect

If D > N, then it's abundant

If D < N, then it's deficient

Divisor Sum = 1 + 3 + 333367

Divisor Sum = 333371

Since our divisor sum of 333371 < 1000101
1000101 is a deficient number!

Odd or Even Test (Parity Function):

A number is even if it is divisible by 2
If not divisible by 2, it is odd

500050.5 =	1000101
	2

Since 500050.5 is not an integer, 1000101 is not divisible by
it is an odd number

This can be written as A(1000101) = Odd

Evil or Odious Test:

Get binary expansion

If binary has even amount 1's, then it's evil

If binary has odd amount 1's, then it's odious

1000101 to binary = 11110100001010100101

There are 10 1's, 1000101 is an evil number

Triangular Test:

Can you stack numbers in a pyramid?
Each row above has one item less than the row before it

Using a bottom row of 1414 items, we cannot form a pyramid
1000101 is not triangular

Triangular number:

Rectangular Test:

Is there an integer m such that n = m(m + 1)

No integer m exists such that m(m + 1) = 1000101
1000101 is not rectangular

Rectangular number:

Automorphic (Curious) Test:

Does n2 ends with n

10001012 = 1000101 x 1000101 = 1000202010201

Since 1000202010201 does not end with 1000101
it is not automorphic (curious)

Automorphic number:

Undulating Test:

Do the digits of n alternate in the form abab

In this case, a = 1 and b = 0

In order to be undulating, Digit 1: 1111111 should be equal to 1

In order to be undulating, Digit 2: 0000000 should be equal to 0

Since our digit pattern does not alternate in our abab pattern1000101 is not undulating

Square Test:

Is there a number m such that m2 = n?

10002 = 1000000 and 10012 = 1002001 which do not equal 1000101

Therefore, 1000101 is not a square

Cube Test:

Is there a number m such that m3 = n

1003 = 1000000 and 1013 = 1030301 ≠ 1000101

Therefore, 1000101 is not a cube

Palindrome Test:

Is the number read backwards equal to the number?

The number read backwards is 1010001

Since 1000101 <> 1010001
it is not a palindrome

Palindromic Prime Test:

Is it both prime and a palindrome

From above, since 1000101 is not both prime and a palindrome
it is NOT a palindromic prime

Repunit Test:

A number is repunit if every digit is equal to 1

Since there is at least one digit in 1000101 ≠ 1
then it is NOT repunit

Apocalyptic Power Test:

Does 2n contain the consecutive digits 666?

21000101 = INF

Since 21000101 does not have 666
1000101 is NOT an apocalyptic power

Pentagonal Test:

It satisfies the form:

n(3n - 1)
2

Check values of 816 and 817

Using n = 817, we have:

817(3(817 - 1)
2

817(2451 - 1)
2

817(2450)
2

1000825 ← Since this does not equal 1000101
this is NOT a pentagonal number

Using n = 816, we have:

816(3(816 - 1)
2

816(2448 - 1)
2

816(2447)
2

998376 ← Since this does not equal 1000101
this is NOT a pentagonal number

Pentagonal number:

Hexagonal Test:

Is there an integer m such that n = m(2m - 1)

No integer m exists such that m(2m - 1) = 1000101
Therefore 1000101 is not hexagonal

Hexagonal number:

Heptagonal Test:

Is there an integer m such that:

m =	n(5n - 3)
	2

No integer m exists such that m(5m - 3)/2 = 1000101
Therefore 1000101 is not heptagonal

Heptagonal number:

Octagonal Test:

Is there an integer m such that n = m(3m - 3)

No integer m exists such that m(3m - 2) = 1000101
Therefore 1000101 is not octagonal

Octagonal number:

Nonagonal Test:

Is there an integer m such that:

m =	n(7n - 5)
	2

No integer m exists such that m(7m - 5)/2 = 1000101
Therefore 1000101 is not nonagonal

Nonagonal number:

Tetrahedral (Pyramidal) Test:

Tetrahederal numbers satisfy the form:

n(n + 1)(n + 2)
6

Check values of 180 and 181

Using n = 181, we have:

181(181 + 1)(181 + 2)
6

181(182)(183)
6

1004731 ← Since this does not equal 1000101
This is NOT a tetrahedral (Pyramidal) number

Using n = 180, we have:

180(180 + 1)(180 + 2)
6

180(181)(182)
6

988260 ← Since this does not equal 1000101
This is NOT a tetrahedral (Pyramidal) number

Narcissistic (Plus Perfect) Test:

Is equal to the square sum of it's m-th powers of its digits

1000101 is a 7 digit number, so m = 7

Square sum of digitsm = 17 + 07 + 07 + 07 + 17 + 07 + 17

Square sum of digitsm = 1 + 0 + 0 + 0 + 1 + 0 + 1

Square sum of digitsm = 3

Since 3 <> 1000101
1000101 is NOT narcissistic (plus perfect)

Catalan Test:

Cn =	2n!
	(n + 1)!n!

Check values of 13 and 14

Using n = 14, we have:

C14 =	(2 x 14)!
	14!(14 + 1)!

Using our factorial lesson

C14 =	28!
	14!15!

C14 =	3.0488834461171E+29
	(87178291200)(1307674368000)

C14 =	3.0488834461171E+29
	1.1400081684828E+23

C14 = 2674440

Since this does not equal 1000101
This is NOT a Catalan number

Using n = 13, we have:

C13 =	(2 x 13)!
	13!(13 + 1)!

Using our factorial lesson

C13 =	26!
	13!14!

C13 =	4.0329146112661E+26
	(6227020800)(87178291200)

C13 =	4.0329146112661E+26
	5.4286103261086E+20

C13 = 742900

Since this does not equal 1000101
This is NOT a Catalan number

Number Properties for 1000101

Final Answer

Positive
Whole
Composite
Deficient
Odd
Evil

You have 1 free calculations remaining

What is the Answer?

Positive
Whole
Composite
Deficient
Odd
Evil

How does the Number Property Calculator work?

Free Number Property Calculator - This calculator determines if an integer you entered has any of the following properties:
* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)
* Evil Numbers or Odious Numbers
* Perfect Numbers, Abundant Numbers, or Deficient Numbers
* Triangular Numbers
* Prime Numbers or Composite Numbers
* Automorphic (Curious)
* Undulating Numbers
* Square Numbers
* Cube Numbers
* Palindrome Numbers
* Repunit Numbers
* Apocalyptic Power
* Pentagonal
* Tetrahedral (Pyramidal)
* Narcissistic (Plus Perfect)
* Catalan
* Repunit
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What 5 formulas are used for the Number Property Calculator?

Positive Numbers are greater than 0
Whole Numbers are positive numbers, including 0, with no decimal or fractional parts
Even numbers are divisible by 2
Odd Numbers are not divisible by 2
Palindromes have equal numbers when digits are reversed

For more math formulas, check out our Formula Dossier

What 11 concepts are covered in the Number Property Calculator?

divisora number by which another number is to be divided.evennarcissistic numbersa given number base b is a number that is the sum of its own digits each raised to the power of the number of digits.numberan arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification. A quantity or amount.number propertyoddpalindromeA word or phrase which reads the same forwards or backwardspentagona polygon of five angles and five sidespentagonal numberA number that can be shown as a pentagonal pattern of dots.
n(3n - 1)/2perfect numbera positive integer that is equal to the sum of its positive divisors, excluding the number itself.propertyan attribute, quality, or characteristic of something

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