A191906 The remainder of (product of proper divisors of n) mod (sum of proper divisors of n).

0, 0, 2, 0, 0, 0, 1, 3, 2, 0, 0, 0, 4, 6, 4, 0, 9, 0, 4, 10, 8, 0, 0, 5, 10, 1, 0, 0, 36, 0, 1, 3, 14, 9, 41, 0, 16, 5, 0, 0, 0, 0, 16, 12, 20, 0, 44, 7, 6, 9, 36, 0, 54, 4, 0, 11, 26, 0, 0, 0, 28, 33, 8, 8, 66, 0, 42, 15, 10, 0, 81, 0, 34, 39, 16, 1, 72, 0, 10, 9, 38, 0, 84, 16, 40, 21

Offset

2,3

Links

Antti Karttunen, Table of n, a(n) for n = 2..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 2..65537

Formula

a(n) = A007956(n) mod A001065(n).

Example

a(2) = 1 mod 1 = 0;
a(3) = 1 mod 1 = 0;
a(4) = 2 mod 3 = 2.

Maple

A007956 := n -> mul(i, i=op(numtheory[divisors](n) minus {1, n}));
A001065 := proc(n) numtheory[sigma](n)-n ; end proc:
A191906 := proc(n) A007956(n) mod A001065(n) ; end proc:
seq(A191906(n), n=2..90) ; # R. J. Mathar, Jun 25 2011

Mathematica

Table[With[{pd=Most[Divisors[n]]}, Mod[Times@@pd, Total[pd]]], {n, 2, 90}] (* Harvey P. Dale, Nov 24 2021 *)

Prog

(PARI) A191906(n) = { my(m=1, s=0); fordiv(n, d, if(d<n, m *= d; s += d)); (m%s); }; \\ Antti Karttunen, Jul 11 2019

Crossrefs

Cf. A001065, A007956, A187680.

Sequence in context: A244233 A227345 A123262 * A371647 A187080 A301342

Adjacent sequences: A191903 A191904 A191905 * A191907 A191908 A191909

Keyword

nonn,look

Author

Juri-Stepan Gerasimov, Jun 19 2011

Status

approved