A191906 - OEIS

%I #18 Nov 24 2021 13:18:46

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A191906/b191906.txt">Table of n, a(n) for n = 2..16384</a>

%H Antti Karttunen, <a href="/A191906/a191906.txt">Data supplement: n, a(n) computed for n = 2..65537</a>

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

%e a(2) = 1 mod 1 = 0;

%e a(3) = 1 mod 1 = 0;

%e a(4) = 2 mod 3 = 2.

%p A007956 := n -> mul(i, i=op(numtheory[divisors](n) minus {1, n}));

%p A001065 := proc(n) numtheory[sigma](n)-n ; end proc:

%p A191906 := proc(n) A007956(n) mod A001065(n) ; end proc:

%p seq(A191906(n),n=2..90) ; # _R. J. Mathar_, Jun 25 2011

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

%o (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

%Y Cf. A001065, A007956, A187680.

%K nonn,look

%O 2,3

%A _Juri-Stepan Gerasimov_, Jun 19 2011