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 A376889 #5 Oct 10 2024 15:35:08
%S A376889 6,60,90,336,5040,87360,764400,11466000,620568000,9478560000,
%T A376889 14217840000,22805874000
%N A376889 Numbers k such that A376888(k) = 2*k.
%C A376889 a(12) > 7*10^10, if it exists.
%C A376889 28279283760000, 282792837600000 and 1583639890560000 are also terms.
%C A376889 k! is a term for k = 3 and 7, and for no other factorial of k < 10^4.
%t A376889 ff[q_, s_] := (q^(s + 1) - 1)/(q - 1); f[p_, e_] := Module[{k = e, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0 || r != 0, If[r > 0, AppendTo[s, {p^(m - 1)!, r}];]; m++]; Times @@ ff @@@ s]; fsigma[1] = 1; fsigma[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[10^6], fsigma[#] == 2*# &]
%o A376889 (PARI) fdigits(n) = {my(k = n, m = 2, r, s = []); while([k, r] = divrem(k, m); k != 0 || r != 0, s = concat(s, r); m++); s;}
%o A376889 fsigma(n) = {my(f = factor(n), p = f[, 1], e = f[, 2], d); prod(i = 1, #p, prod(j = 1, #d=fdigits(e[i]), (p[i]^(j!*(d[j]+1)) - 1)/(p[i]^j! - 1)));}
%o A376889 is(k) = fsigma(k) == 2*k;
%Y A376889 Cf. A376888.
%Y A376889 Subsequence of A023196.
%Y A376889 Similar sequences: A007357, A038182, A074849, A097464, A331108, A331111.
%K A376889 nonn,base,more
%O A376889 1,1
%A A376889 _Amiram Eldar_, Oct 08 2024