A187680 a(n) = (product of divisors of n) mod (sum of divisors of n).

0, 2, 3, 1, 5, 0, 7, 4, 1, 10, 11, 20, 13, 4, 9, 1, 17, 21, 19, 20, 25, 16, 23, 36, 1, 4, 9, 0, 29, 0, 31, 8, 33, 22, 25, 83, 37, 4, 9, 40, 41, 48, 43, 8, 21, 28, 47, 88, 1, 8, 9, 76, 53, 96, 1, 16, 49, 34, 59, 120, 61, 4, 31, 1

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 17 2011

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203, A007955, A145551, A188061.

Programs

Maple

A187680 := proc(n) A007955(n) mod numtheory[sigma](n) ; end proc:
seq(A187680(n),n=1..120) ; # R. J. Mathar, Mar 17 2011

Mathematica

Table[Mod[Times@@Divisors[n],DivisorSigma[1,n]],{n,70}] (* Harvey P. Dale, May 23 2021 *)
a[n_] := Mod[n^(DivisorSigma[0, n]/2), DivisorSigma[1, n]]; Array[a, 60] (* Amiram Eldar, Jun 18 2022 *)

PARI

a(n) = my(d=divisors(n)); vecprod(d) % vecsum(d); \\ Michel Marcus, Jan 29 2019

Formula

a(n) = A007955(n) mod A000203(n).

a(n) = 0 iff n is in A145551 and a(n) = 1 iff n is in A188061. - Amiram Eldar, Jun 18 2022