cp's OEIS Frontend

A191581 Numbers whose sum of their anti-divisors divides the sum of their divisors.

%I A191581 #26 May 09 2021 08:15:58
%S A191581 3,6,11,22,30,33,65,82,117,218,354,483,508,537,3276,6430,21541,117818,
%T A191581 130356,753612,1007328,2113416,2379540,3589646,7231219,7346148,
%U A191581 8515767,13050345,20199648,34424166,44575896,47245905,50414595,104335023,217728002,1217532421
%N A191581 Numbers whose sum of their anti-divisors divides the sum of their divisors.
%C A191581 A161917 is a subsequence of this sequence.
%F A191581 {n: A066417(n) | A000203(n)}. - _R. J. Mathar_, Oct 01 2011
%e A191581 6-> sum divisors=sigma(6)=12; sum anti-divisors=4; 12/4=3.
%e A191581 30-> sum divisors=sigma(30)=72; sum anti-divisors=4+12+20=36; 72/36=2.
%p A191581 with(numtheory): P:=proc(i) local a, b, j, k, s, n;
%p A191581 for n from 3 to i do b:=divisors(n); s:=add(b[k],k=1..nops(b));
%p A191581 k:=0; j:=n; while j mod 2 <> 1 do k:=k+1; j:=j/2; od; a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
%p A191581 if type(s/a,integer) then print(n); fi; od; end: P(10^6);
%t A191581 f[n_] := Total@ Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]; Select[Range[3, 10^3], Mod[DivisorSigma[1, #], f@ #] == 0 &] (* _Michael De Vlieger_, Oct 08 2015 *)
%Y A191581 Cf. A000203, A066272, A066417, A161917, A191580.
%K A191581 nonn,easy
%O A191581 1,1
%A A191581 _Paolo P. Lava_, Jun 07 2011
%E A191581 a(21)-a(36) from _Donovan Johnson_, Jun 24 2012