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 A358280 #19 Aug 30 2023 02:00:50 %S A358280 1,2,3,8,25,124,721,5048,40323,362906,3628801,39916930,479001601, %T A358280 6227021522,87178291227,1307674373048,20922789888001,355687428136444, %U A358280 6402373705728001,121645100409194912,2432902008176640723,51090942171713068802,1124000727777607680001 %N A358280 a(n) = Sum_{d|n} (d-1)!. %F A358280 G.f.: Sum_{k>0} (k-1)! * x^k/(1 - x^k). %F A358280 If p is prime, a(p) = 1 + (p-1)!. %t A358280 a[n_] := DivisorSum[n, (# - 1)! &]; Array[a, 23] (* _Amiram Eldar_, Aug 30 2023 *) %o A358280 (PARI) a(n) = sumdiv(n, d, (d-1)!); %o A358280 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, (k-1)!*x^k/(1-x^k))) %Y A358280 Cf. A062363, A321875. %Y A358280 Cf. A038507, A358279. %K A358280 nonn,easy %O A358280 1,2 %A A358280 _Seiichi Manyama_, Nov 08 2022