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 A354863 #20 Aug 30 2023 02:00:32
%S A354863 1,5,19,121,601,5641,35281,406561,3447361,45420481,439084801,
%T A354863 7565564161,80951270401,1525654690561,20737536019201,421943967244801,
%U A354863 6046686277632001,150482493928166401,2311256907767808001,61410502863943833601,1132546296081328128001
%N A354863 a(n) = n! * Sum_{d|n} (n/d) / d!.
%F A354863 E.g.f.: Sum_{k>0} k * (exp(x^k) - 1).
%F A354863 If p is prime, a(p) = 1 + p * p!.
%t A354863 a[n_] := n! * DivisorSum[n, (n/#) / #! &]; Array[a, 21] (* _Amiram Eldar_, Aug 30 2023 *)
%o A354863 (PARI) a(n) = n!*sumdiv(n, d, n/d/d!);
%o A354863 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, k*(exp(x^k)-1))))
%o A354863 (Python)
%o A354863 from math import factorial
%o A354863 from sympy import divisors
%o A354863 def A354863(n):
%o A354863 f = factorial(n)
%o A354863 return sum(f*n//d//factorial(d) for d in divisors(n,generator=True)) # _Chai Wah Wu_, Jun 09 2022
%Y A354863 Cf. A057625, A354843, A354862.
%K A354863 nonn
%O A354863 1,2
%A A354863 _Seiichi Manyama_, Jun 09 2022