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

Author

Juri-Stepan Gerasimov, Jun 19 2011

Keywords

• nonn
• look

Examples

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

Links

• Antti Karttunen, Table of n, a(n) for n = 2..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 2..65537

Crossrefs

Cf. A001065, A007956, A187680.

Programs

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 *)

PARI

A191906(n) = { my(m=1,s=0); fordiv(n, d, if(dAntti Karttunen, Jul 11 2019

Formula

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