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 A354900 #15 Jun 11 2022 07:52:33 %S A354900 1,9,163,6193,375001,33602521,4150656721,676462516801,140587148681281, %T A354900 36288005670120961,11388728893445164801,4270826391670469473921, %U A354900 1886009588552176549862401,968725766890781857146309121,572622616354852243874626732801 %N A354900 a(n) = n! * Sum_{d|n} d^d / (n/d)!. %F A354900 E.g.f.: Sum_{k>0} k^k * (exp(x^k) - 1). %F A354900 If p is prime, a(p) = 1 + p^p * p!. %t A354900 a[n_] := n! * DivisorSum[n, #^#/(n/#)! &]; Array[a, 15] (* _Amiram Eldar_, Jun 11 2022 *) %o A354900 (PARI) a(n) = n!*sumdiv(n, d, d^d/(n/d)!); %o A354900 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, k^k*(exp(x^k)-1)))) %Y A354900 Cf. A057625, A354843, A354888, A354892, A354899. %K A354900 nonn %O A354900 1,2 %A A354900 _Seiichi Manyama_, Jun 11 2022