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

1,1

Comments

A161917 is a subsequence of this sequence.

Links

Table of n, a(n) for n=1..36.

Formula

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A293066 A104253 A283668 * A192896 A115030 A228206

Adjacent sequences: A191578 A191579 A191580 * A191582 A191583 A191584

Keyword

nonn,easy

Author

Paolo P. Lava, Jun 07 2011

Extensions

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

Status

approved