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 A360948 #17 Jul 31 2023 02:25:21 %S A360948 1,3,4,11,6,41,8,89,100,182,12,1088,14,723,2592,3697,18,11804,20, %T A360948 29289,30382,13037,24,246912,78776,58554,374248,687929,30,2567895,32, %U A360948 3431585,4640462,1182284,6265548,37037563,38,5246529,55878240,128618380,42,266983306,44 %N A360948 a(n) = Sum_{d|n} (n/d)^(d-1) * binomial(d+n/d-1,d). %F A360948 G.f.: Sum_{k>0} (1/k) * (1/(1 - k * x^k)^k - 1). %F A360948 If p is prime, a(p) = 1 + p. %t A360948 a[n_] := DivisorSum[n, (n/#)^(#-1) * Binomial[# + n/# - 1, #] &]; Array[a, 50] (* _Amiram Eldar_, Jul 31 2023 *) %o A360948 (PARI) a(n) = sumdiv(n, d, (n/d)^(d-1)*binomial(d+n/d-1, d)); %o A360948 (PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, (1/(1-k*x^k)^k-1)/k)) %Y A360948 Cf. A338662, A360794. %K A360948 nonn %O A360948 1,2 %A A360948 _Seiichi Manyama_, Feb 26 2023