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 A068978 #40 Apr 19 2025 04:05:27
%S A068978 1,2,9,18,105,210,24375,48750,133848,18780741,18780965,37561482,
%T A068978 37561930,121486365,169028685,242972730,338057370,360988056,676114740,
%U A068978 1120584213,1285201500,1352229480,2241168426,2776831200,5352575025,5408917920,7437262140,10705150050
%N A068978 Numbers k such that Sum_{d|k} tau(d)/d is an integer, where tau(x) = A000005(x).
%C A068978 Also k such that k divides A007429(k).
%C A068978 Also k such that k divides A211780(k). - _Jaroslav Krizek_, Sep 28 2014
%C A068978 a(28) > 10^10. - _Giovanni Resta_, Jun 10 2013
%C A068978 a(33) > 5*10^10. - _Hiroaki Yamanouchi_, Oct 05 2014
%H A068978 Hiroaki Yamanouchi, <a href="/A068978/b068978.txt">Table of n, a(n) for n = 1..32</a>
%H A068978 Hiroaki Yamanouchi, <a href="/A068978/a068978.txt">Conjectured table of n, a(n) for n = 1..200</a>
%t A068978 t = {}; n = 0; While[n++ <= 20000000, If[Mod[Total[DivisorSigma[1, Divisors[n]]], n] == 0, AppendTo[t, n]]]; t (* _Jayanta Basu_, Apr 03 2013 *)
%t A068978 f[p_, e_] := (p*(p^(e+1) - 1) - (p-1)*(e+1))/(p-1)^2; q[1] = True; q[k_] := Divisible[Times @@ f @@@ FactorInteger[k], k]; Select[Range[200000], q] (* _Amiram Eldar_, Apr 19 2025 *)
%o A068978 (PARI) for(n=1, 20000000, if(denominator( sumdiv(n,d, numdiv(d)/d)) ==1, print1(n,",")))
%o A068978 (PARI) isok(k) = {my(f = factor(k)); !(prod(i = 1, #f~, p = f[i, 1]; e = f[i, 2]; (p*(p^(e+1) - 1) - (p-1)*(e+1))/(p-1)^2) % k);} \\ _Amiram Eldar_, Apr 19 2025
%Y A068978 Cf. A000005, A007429, A211780.
%K A068978 nonn
%O A068978 1,2
%A A068978 _Benoit Cloitre_, Apr 06 2002
%E A068978 More terms from _Rick L. Shepherd_, Jun 23 2002
%E A068978 a(12)-a(27) from _Giovanni Resta_, Jun 10 2013
%E A068978 a(28) from _Hiroaki Yamanouchi_, Oct 05 2014