A081756 - OEIS

%I #25 Feb 23 2024 07:26:11

%S 1,12,56,360,992,2016,16256,120960,131040,1571328,8714160,67100672,

%T 94279680,182131200,571963392,1379454720,4428914688,5517818880,

%U 17179738112,70912195200,153003540480,159991977600,175445913600,265734881280,274877382656,612014161920

%N Numbers n such that there is a proper divisor d of n satisfying sigma(d)=n.

%C A139256 is a subsequence. - _Michel Marcus_, Dec 02 2013

%H Ray Chandler, <a href="/A081756/b081756.txt">Table of n, a(n) for n = 1..1000</a> (using comment in formula section from _David Wasserman_ and b-files for A007691 and A054030)

%F Multiply A007691 by A054030 and sort the resulting sequence. - _David Wasserman_, Jun 28 2004

%t kmax = 10^12;

%t A007691 = Cases[Import["https://oeis.org/A007691/b007691.txt", "Table"], {_, _}][[All, 2]];

%t A054030 = Cases[Import["https://oeis.org/A054030/b054030.txt", "Table"], {_, _}][[All, 2]];

%t okQ[n_] := AnyTrue[Most[Divisors[n]], DivisorSigma[1, #] == n&];

%t {1}~Join~Reap[Do[k = A007691[[i]]*A054030[[j]]; If[k <= kmax, Sow[k]], {i, Length[A007691]}, {j, Length[A054030]}]][[2, 1]] // Union // Select[#, okQ]& (* _Jean-François Alcover_, Oct 31 2019, after _David Wasserman_ *)

%Y Cf. A007691, A054030, A065125, A139256.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Apr 08 2003

%E More terms from _David Wasserman_, Jun 28 2004

%E Description clarified by _Ray Chandler_, May 18 2017