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.
%I A066290 #13 Aug 20 2023 16:57:35
%S A066290 1,10,60,65,130,150,260,780,1105,2210,4420,8840,13260,19720,20737,
%T A066290 32045,41474,55250,64090,82948,103685,128180,207370,207553,221000,
%U A066290 248844,256360,295800,331500,352529,384540,414740,415106,450840,512720,705058,829480,830212
%N A066290 Numbers m such that DivisorSigma(4*k-2, m) mod m = 0 holds presumably for all k; that is, (4k-2)-power-sums of divisors of m are divisible by m for all k.
%F A066290 DivisorSigma(4k-2, m)/m is an integer for k = 1, 2, 3, .., 200, ...
%e A066290 Tested for each m and k < 200. Proof for several values of k seems not so tedious because the number of divisors of the terms of the sequence is not so large: {1, 4, 12, 4, 8, 12, 12, 24, 8, 16, 24, 32, 48, 32, 4, 16, 8, 32, 32, 12, 8, 48, 16, 8, 64, 24, 64, 96, 96, 8, 96, 24, 16, 96, 80, 16, 32, 24}.
%t A066290 lastSeq = {}; max = 100; While[seq = Reap[For[n = 1, n < 10^6, n++, If[AllTrue[Range[max], Mod[DivisorSigma[4 # - 2, n], n] == 0&], Print[n]; Sow[n]]]][[2, 1]]; seq != lastSeq, lastSeq = seq; max = max + 100; Print["max = ", max]]; seq (* _Jean-François Alcover_, Oct 02 2016 *)
%Y A066290 Cf. A066135, A066284, A066289.
%K A066290 nonn
%O A066290 1,2
%A A066290 _Labos Elemer_, Dec 12 2001
%E A066290 More terms from _Jean-François Alcover_, Oct 02 2016