A323155 a(n) = Product_{d|n, d-1 is prime} (d-1)^(1+A286561(n,d-1)), where A286561(n,k) gives the k-valuation of n (for k > 1).

1, 1, 2, 3, 1, 20, 1, 21, 2, 1, 1, 3960, 1, 13, 2, 21, 1, 340, 1, 57, 2, 1, 1, 1275120, 1, 1, 2, 39, 1, 2900, 1, 651, 2, 1, 1, 201960, 1, 37, 2, 399, 1, 10660, 1, 129, 2, 1, 1, 119861280, 1, 1, 2, 3, 1, 18020, 1, 1911, 2, 1, 1, 643678200, 1, 61, 2, 651, 1, 20, 1, 201, 2, 13, 1, 4617209520, 1, 73, 2, 111, 1, 20, 1, 31521, 2, 1, 1, 175186440, 1, 1, 2, 903, 1

Offset: 1

Author

Antti Karttunen, Jan 09 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A010051, A286561, A323156, A323157.

Cf. also A185633.

Programs

PARI

A323155(n) = { my(m=1); fordiv(n, d, if(isprime(d-1), m *= (d-1)^(1+valuation(n,d-1)))); (m); }; \\ Antti Karttunen, Jan 09 2019

Formula

a(n) = Product_{d|n, d>2} [(d-1)^(1+A286561(n,d-1))]^A010051(d-1).