cp's OEIS Frontend

A355887 a(n) = Sum_{k=1..n} k^k * floor(n/k).

%I A355887 #22 Jul 21 2022 15:22:49
%S A355887 1,6,34,295,3421,50109,873653,17651130,405071647,10405074777,
%T A355887 295716745389,9211817240589,312086923832843,11424093750214407,
%U A355887 449317984131076935,18896062057857406028,846136323944194170206,40192544399241119212807
%N A355887 a(n) = Sum_{k=1..n} k^k * floor(n/k).
%H A355887 Seiichi Manyama, <a href="/A355887/b355887.txt">Table of n, a(n) for n = 1..386</a>
%F A355887 a(n) = Sum_{k=1..n} Sum_{d|k} d^d.
%F A355887 G.f.: (1/(1-x)) * Sum_{k>0} (k * x)^k/(1 - x^k).
%o A355887 (PARI) a(n) = sum(k=1, n, n\k*k^k);
%o A355887 (PARI) a(n) = sum(k=1, n, sumdiv(k, d, d^d));
%o A355887 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-x^k))/(1-x))
%o A355887 (Python)
%o A355887 def A355887(n): return n*(1+n**(n-1))+sum(k**k*(n//k) for k in range(2,n)) if n>1 else 1 # _Chai Wah Wu_, Jul 21 2022
%Y A355887 Partial sums of A062796.
%Y A355887 Cf. A006218, A024916, A064602, A064603, A064604, A248076, A319194.
%K A355887 nonn
%O A355887 1,2
%A A355887 _Seiichi Manyama_, Jul 20 2022