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

3, 6, 11, 22, 30, 33, 65, 82, 117, 218, 354, 483, 508, 537, 3276, 6430, 21541, 117818, 130356, 753612, 1007328, 2113416, 2379540, 3589646, 7231219, 7346148, 8515767, 13050345, 20199648, 34424166, 44575896, 47245905, 50414595, 104335023, 217728002, 1217532421

Offset: 1

Author

Paolo P. Lava, Jun 07 2011

Keywords

• nonn
• easy

Comments

A161917 is a subsequence of this sequence.

Examples

			6-> sum divisors=sigma(6)=12; sum anti-divisors=4; 12/4=3.
30-> sum divisors=sigma(30)=72; sum anti-divisors=4+12+20=36; 72/36=2.
		

Crossrefs

Cf. A000203, A066272, A066417, A161917, A191580.

Programs

Maple

with(numtheory): P:=proc(i) local a, b, j, k, s, n;
for n from 3 to i do b:=divisors(n); s:=add(b[k],k=1..nops(b));
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;
if type(s/a,integer) then print(n); fi; od; end: P(10^6);

Mathematica

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 *)

Formula

{n: A066417(n) | A000203(n)}. - R. J. Mathar, Oct 01 2011

Extensions

a(21)-a(36) from Donovan Johnson, Jun 24 2012