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 A352014 #13 Oct 04 2023 03:55:20
%S A352014 0,1,1,-6,1,60,1,-5040,20160,347760,1,-59875200,1,6218372160,
%T A352014 47221574400,-1307674368000,1,177843714048000,1,-126713646259200000,
%U A352014 1219830034655232000,51090928092415411200,1,-38778025108327464960000,25852016738884976640000
%N A352014 a(n) = Sum_{p|n, p prime} (-1)^(n/p+1) * (n-1)!/(p-1)!.
%F A352014 E.g.f.: Sum_{p prime} log(1+x^p)/p!.
%t A352014 a[n_] := Sum[(-1)^(n/p + 1)*(n - 1)!/(p - 1)!, {p, FactorInteger[n][[;; , 1]]}]; a[1] = 0; Array[a, 25] (* _Amiram Eldar_, Oct 04 2023 *)
%o A352014 (PARI) a(n) = sumdiv(n, d, isprime(d)*(-1)^(n/d+1)*(n-1)!/(d-1)!);
%o A352014 (PARI) my(N=40, x='x+O('x^N)); concat(0, Vec(serlaplace(sum(k=1, N, isprime(k)*log(1+x^k)/k!))))
%Y A352014 Cf. A352005, A352012, A352013.
%K A352014 sign
%O A352014 1,4
%A A352014 _Seiichi Manyama_, Feb 28 2022