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 A319112 #12 Feb 27 2022 12:02:19
%S A319112 1,0,1,2,6,44,170,1644,7448,72624,653112,8510160,62704752,1324662624,
%T A319112 10772812752,167386388064,2413326453120,52610523489024,
%U A319112 597065112874368,18066985168806144,212119023906342144,4734822914239173120,100734270778298352384,2818116390408742291968,48201015565806837709824
%N A319112 Expansion of e.g.f. Product_{k>=1} 1/(1 - x^prime(k)/prime(k)).
%F A319112 E.g.f.: exp(Sum_{k>=1} ( Sum_{p|k, p prime} p^(1-k/p) ) * x^k/k).
%p A319112 seq(n!*coeff(series(mul(1/(1-x^ithprime(k)/ithprime(k)),k=1..100),x=0,25),x,n),n=0..24); # _Paolo P. Lava_, Jan 09 2019
%t A319112 nmax = 24; CoefficientList[Series[Product[1/(1 - x^Prime[k]/Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t A319112 nmax = 24; CoefficientList[Series[Exp[Sum[Sum[Boole[PrimeQ[d]] d^(1 - k/d), {d, Divisors[k]}] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%t A319112 a[n_] := a[n] = If[n == 0, 1, (n - 1)! Sum[Sum[Boole[PrimeQ[d]] d^(1 - k/d), {d, Divisors[k]}] a[n - k]/(n - k)!, {k, 1, n}]]; Table[a[n], {n, 0, 24}]
%o A319112 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, 1-isprime(k)*x^k/k))) \\ _Seiichi Manyama_, Feb 27 2022
%Y A319112 Cf. A002098, A007841, A319113.
%K A319112 nonn
%O A319112 0,4
%A A319112 _Ilya Gutkovskiy_, Sep 10 2018