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%I #20 Mar 27 2022 03:09:42
%S 1,2,3,8,9,10,11,16,17,18,19,24,25,26,27,32,33,34,35,40,41,42,43,48,
%T 49,50,78,83,84,85,86,91,92,93,94,99,100,101,102,107,108,109,110,115,
%U 116,117,118,123,124,125,126,131,132,160,161,166,167,168,169,174,175,176,177,182,183,184
%N a(n) = Sum_{k=1..n} k^k * floor(n/k^k).
%C What is the limit_{n->infinity} a(n) / (n*log(n)/LambertW(log(n))) ?. - _Vaclav Kotesovec_, Aug 30 2021
%H Seiichi Manyama, <a href="/A347397/b347397.txt">Table of n, a(n) for n = 1..10000</a>
%H Vaclav Kotesovec, <a href="/A347397/a347397.jpg">Plot of a(n) / (n*log(n)/LambertW(log(n))) for n = 1..10000</a>
%F G.f.: (1/(1 - x)) * Sum_{k>=1} k^k * x^(k^k)/(1 - x^(k^k)).
%t Table[Sum[k^k*Floor[n/k^k], {k, 1, n}], {n, 1, 100}] (* _Vaclav Kotesovec_, Aug 30 2021 *)
%o (PARI) a(n) = sum(k=1, n, k^k*(n\k^k));
%Y Cf. A024916, A062071, A309125, A309126, A309127.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Aug 30 2021
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