A069783 a(n) = gcd(d(n!^3), d(n!)), where d() is the number of divisors function.

1, 2, 4, 8, 16, 2, 4, 32, 32, 10, 20, 8, 16, 32, 448, 448, 1792, 32, 64, 80, 3200, 1280, 2560, 320, 448, 1792, 25088, 101920, 203840, 128, 256, 4096, 81920, 112640, 2048, 8960, 17920, 1024, 2048, 5120, 10240, 5734400, 11468800, 1003520, 250880, 8960, 17920

Offset: 1

Author

Labos Elemer, Apr 08 2002

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A000142, A069780, A069781, A069782.

Programs

Mathematica

Table[GCD[DivisorSigma[0, (n!)^3], DivisorSigma[0, n! ]], {n, 1, 100}]

PARI

a(n) = my(e = factor(n!)[, 2]); gcd(vecprod(apply(x -> x + 1, e)), vecprod(apply(x -> 3*x + 1, e))) \\ Amiram Eldar, Mar 07 2025

Formula

a(n) = A069780(n!).