cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A068986 Numbers k such that Sum_{d|k} sigma(d)/d is an integer.

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%I A068986 #41 Dec 29 2024 03:42:20
%S A068986 1,21,105,1050,1155,24921,26565,45150,49842,59455,249210,274131,
%T A068986 548262,1129645,1151325,1248555,1309350,2302650,2741310,3388935,
%U A068986 4605300,6305013,12610026,13417131,14685385,23722545,25750550,26834262,30154410,33388425,42997750,44056155
%N A068986 Numbers k such that Sum_{d|k} sigma(d)/d is an integer.
%C A068986 Also numbers k that divide A060640(k). - _Seiichi Manyama_, May 08 2021
%H A068986 Amiram Eldar, <a href="/A068986/b068986.txt">Table of n, a(n) for n = 1..100</a> (terms 1..64 from Michel Marcus)
%t A068986 f[p_, e_] := ((e + 1)*p^(e + 2) - (e + 2)*p^(e + 1) + 1)/(p - 1)^2; q[1] = True; q[n_] := Divisible[Times @@ f @@@ FactorInteger[n], n]; Select[Range[10^6], q] (* _Amiram Eldar_, Dec 29 2024 *)
%o A068986 (PARI) for(n=1,10^7,if(frac(sumdiv(n,d, sigma(d)/d))==0,print1(n,",")))
%o A068986 (PARI) is(k) = {my(f = factor(k)); !(prod(i = 1, #f~, p = f[i, 1]; e = f[i, 2];  ((e + 1)*p^(e + 2) - (e + 2)*p^(e + 1) + 1)/(p - 1)^2) % k);} \\ _Amiram Eldar_, Dec 29 2024
%Y A068986 Cf. A000203, A060640, A017665, A017666.
%K A068986 nonn
%O A068986 1,2
%A A068986 _Benoit Cloitre_, Apr 06 2002
%E A068986 More terms from _Jason Earls_, Apr 09 2002
%E A068986 a(22)-a(25) from _Jinyuan Wang_, Apr 06 2020
%E A068986 a(26)-a(32) from _Michel Marcus_, Apr 06 2020