9972
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 27
- Digital Root
- 9
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 18
- Divisor Sum
- 25298
- Proper Divisor Sum (Aliquot Sum)
- 15326
- 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
- 3312
- Möbius Function
- 0
- Radical
- 1662
- Omega Function (Ω)
- 5
- Little Omega Function (ω)
- 3
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
- no
- Narcissistic Number
- no
- Collatz Steps
- 135
- Smith Number
- no
- Vampire 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
- no
- Achilles Number
- no
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- yes
- Odd
- no
Appears in sequences
- Number of partitions into non-integral powers.at n=38A000327
- Number of proper factorizations of p1^n*p2^3, where p1 and p2 are distinct primes.at n=17A031126
- Decimal part of a(n)^(1/n) starts with a pandigital anagram (digits 0 through 9 in some order).at n=36A035304
- Row 4 of array in A047666.at n=12A047668
- T(n,4), array T as in A054134.at n=7A054138
- Numbers k such that k^512 + 1 is prime.at n=28A057465
- McKay-Thompson series of class 36A for Monster.at n=41A058644
- McKay-Thompson series of class 36D for the Monster simple group.at n=41A058647
- Convolution of L(n+1) := A000204(n+1) (Lucas), n>=0, with L(n+2), n>=0.at n=11A067980
- (Sum of digits of n)^4 - (sum of digits of n^4).at n=28A069978
- (Sum of digits of n)^4 - (sum of digits of n^4).at n=37A069978
- Numbers k such that k^4 + 1, (k+2)^4 + 1 and (k+4)^4 + 1 are all primes.at n=9A073476
- a(n) = n*(n^4 + 30*n^3 + 395*n^2 + 2910*n + 11064)/120.at n=10A090391
- Number of partitions of n in which each odd part has odd multiplicity and each even part has even multiplicity.at n=54A102247
- Expansion of chi(-q^3) / chi^3(-q) in powers of q where chi() is a Ramanujan theta function.at n=20A128128
- Expansion of f(q, q^2) * f(-q^3) / f(-q^2)^2 in powers of q where f(, ), f() are Ramanujan theta functions.at n=40A132180
- Expansion of chi(q)^3 / chi(q^3) in powers of q where chi() is a Ramanujan theta function.at n=40A132972
- Expansion of phi(q) * phi(-q^18) / (phi(-q^3) * phi(-q^6)) in powers of q where phi() is a Ramanujan theta function.at n=40A139213
- Expansion of b(q) / b(q^2) in powers of q where b() is a cubic AGM theta function.at n=40A141094
- Row sums of A163233 and A163235.at n=23A163242