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 A338662 #19 May 09 2021 13:34:32 %S A338662 1,5,10,29,26,123,50,305,352,668,122,3844,170,2593,9704,13825,290, %T A338662 41598,362,118259,107986,33047,530,929102,394376,130744,1203580, %U A338662 2737415,842,9910225,962,13315073,14199222,2404670,33547310,136502007,1370,10555795,168405072,548460064,1682 %N A338662 a(n) = Sum_{d|n} (n/d)^d * binomial(d+n/d-1, d). %H A338662 Seiichi Manyama, <a href="/A338662/b338662.txt">Table of n, a(n) for n = 1..5000</a> %F A338662 G.f.: Sum_{k >= 1} (1/(1 - k * x^k)^k - 1). %F A338662 If p is prime, a(p) = 1 + p^2. %t A338662 a[n_] := DivisorSum[n, (n/#)^# * Binomial[# + n/# - 1, #] &]; Array[a, 40] (* _Amiram Eldar_, Apr 22 2021 *) %o A338662 (PARI) a(n) = sumdiv(n, d, (n/d)^d*binomial(d+n/d-1, d)); %o A338662 (PARI) N=66; x='x+O('x^N); Vec(sum(k=1, N, 1/(1-k*x^k)^k-1)) %Y A338662 Cf. A081543, A338663, A343574. %K A338662 nonn %O A338662 1,2 %A A338662 _Seiichi Manyama_, Apr 22 2021