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A191581 Numbers whose sum of their anti-divisors divides the sum of their divisors. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 25 12:15 EDT 2021. Contains 346290 sequences. (Running on oeis4.)