A069783 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

FORMULA

a(n) = A069780(n!).

MATHEMATICA

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

PROG

(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

CROSSREFS