72
domain: N
Properties
Digital Properties
- Digit Count
- 2
- Digit Sum
- 9
- Digital Root
- 9
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 12
- Divisor Sum
- 195
- Proper Divisor Sum (Aliquot Sum)
- 123
- 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
- 24
- Möbius Function
- 0
- Radical
- 6
- Omega Function (Ω)
- 5
- 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
- yes
Recreational
- Happy Number
- no
- Harshad Number
- yes
- Narcissistic Number
- no
- Collatz Steps
- 22
- Smith Number
- no
Classification
- Natural
- yes
- Even
- yes
- Odd
- 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
Names
- German
- zweiundsiebzig· ordinal: zweiundsiebzigste
- English
- seventy-two· ordinal: seventy-second
- Spanish
- setenta y dos· ordinal: 72º
- French
- soixante-douze· ordinal: soixante-douzième
- Italian
- settantadue· ordinal: 72º
- Latin
- septuaginta duo· ordinal: 72.
- Portuguese
- setenta e dois· ordinal: 72º
Appears in sequences
- The positive integers. Also called the natural numbers, the whole numbers or the counting numbers, but these terms are ambiguous.at n=71A000027
- Let k = p_1^e_1 p_2^e_2 p_3^e_3 ... be the prime factorization of n. Sequence gives k such that the sum of the numbers of 1's in the binary expansions of e_1, e_2, e_3, ... is odd.at n=34A000028
- Numbers that are not squares (or, the nonsquares).at n=63A000037
- 1-digit numbers arranged in alphabetical order, then the 2-digit numbers arranged in alphabetical order, then the 3-digit numbers, etc.at n=65A000052
- Local stops on New York City 1 Train (Broadway-7 Avenue Local) subway.at n=9A000053
- Local stops on New York City A line subway.at n=7A000054
- Generalized tangent numbers d(n,1).at n=32A000061
- A Beatty sequence: a(n) = floor(n/(e-2)).at n=51A000062
- Number of positive integers <= 2^n of form x^2 + 4 y^2.at n=8A000072
- a(n) = n^2*Product_{p|n} (1 + 1/p).at n=5A000082
- Number of transformation groups of order n.at n=29A000113
- Number of transformation groups of order n.at n=45A000113
- Number of transformation groups of order n.at n=50A000113
- Number of transformation groups of order n.at n=54A000113
- Number of transformation groups of order n.at n=59A000113
- Number of cusps of principal congruence subgroup Gamma^{hat}(n).at n=12A000114
- Denumerants: Expansion of 1/((1-x)*(1-x^2)*(1-x^5)).at n=34A000115
- Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2 = A001622.at n=44A000201
- a(n) = sigma(n), the sum of the divisors of n. Also called sigma_1(n).at n=29A000203
- a(n) = sigma(n), the sum of the divisors of n. Also called sigma_1(n).at n=45A000203