972
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 18
- Digital Root
- 9
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 18
- Divisor Sum
- 2548
- Proper Divisor Sum (Aliquot Sum)
- 1576
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Highly Composite
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 324
- Möbius Function
- 0
- Radical
- 6
- Omega Function (Ω)
- 7
- Little Omega Function (ω)
- 2
Special
- Factorial
- no
- Catalan Number
- no
- Bell Number
- no
- Motzkin Number
- no
- Primorial
- no
Figurate Numbers
- Fibonacci Number
- no
- Triangular Number
- no
- Perfect Square
- no
- Perfect Cube
- no
- Pentagonal Number
- no
- Hexagonal Number
- no
- Lucas Number
- no
- Tetrahedral Number
- no
- Pell Number
- no
- Tribonacci Number
- no
- Pronic Number
- no
Recreational
- Happy Number
- no
- Harshad Number
- yes
- Narcissistic Number
- no
- Collatz Steps
- 98
- Smith Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- no
- Squarefree Number
- no
- Prime Power
- no
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- yes
- Achilles Number
- yes
- Perfect Power
- no
- Smooth Number
- yes
- Carmichael Number
- no
Classification
- Even
- yes
- Odd
- no
Names
- German
- neunhundertzweiundsiebzig· ordinal: neunhundertzweiundsiebzigste
- English
- nine hundred seventy-two· ordinal: nine hundred seventy-second
- Spanish
- novecientos setenta y dos· ordinal: 972º
- French
- neuf cent soixante-douze· ordinal: neuf cent soixante-douzième
- Italian
- novecentosettantadue· ordinal: 972º
- Latin
- nongenti septuaginta duo· ordinal: 972.
- Portuguese
- novecentos e setenta e dois· ordinal: 972º
Appears in sequences
- Partial sums of (unordered) ways of making change for n cents using coins of 1, 2, 5, 10 cents.at n=30A000064
- a(n) = n^2*Product_{p|n} (1 + 1/p).at n=26A000082
- Number of cusps of principal congruence subgroup Gamma^{hat}(n).at n=52A000114
- a(n) is smallest number > a(n-1) of form a(i)*a(j), i < j < n.at n=25A000423
- Number of compositions of n into 3 ordered relatively prime parts.at n=51A000741
- a(n) = max{(n - i)*a(i) : i < n}; a(0) = 1.at n=19A000792
- a(n+1) = n*a(n) + a(n-1) with a(0)=1, a(1)=0.at n=7A001053
- Double-bitters: only even length runs in binary expansion.at n=26A001196
- Number of partitions of n into at most 4 parts.at n=47A001400
- Powerful numbers, definition (1): if a prime p divides n then p^2 must also divide n (also called squareful, square full, square-full or 2-powerful numbers).at n=52A001694
- Numbers k such that 17*2^k - 1 is prime.at n=19A001774
- A self-generating sequence: every positive integer occurs as a(i)-a(j) for a unique pair i,j.at n=14A001856
- Apply partial sum operator twice to Fibonacci numbers.at n=12A001924
- Expansion of a modular function for Gamma_0(21).at n=14A002511
- Coefficients for numerical integration.at n=4A002685
- Numbers that are the sum of 4 positive 5th powers.at n=14A003349
- 3-smooth numbers: numbers of the form 2^i*3^j with i, j >= 0.at n=39A003586
- Smallest positive integer that is n times its digit sum, or 0 if no such number exists.at n=53A003634
- Expansion of (1+x)/(1-3*x).at n=6A003946
- Numbers that are the sum of at most 4 positive 5th powers.at n=34A004844