A347397 a(n) = Sum_{k=1..n} k^k * floor(n/k^k).

1, 2, 3, 8, 9, 10, 11, 16, 17, 18, 19, 24, 25, 26, 27, 32, 33, 34, 35, 40, 41, 42, 43, 48, 49, 50, 78, 83, 84, 85, 86, 91, 92, 93, 94, 99, 100, 101, 102, 107, 108, 109, 110, 115, 116, 117, 118, 123, 124, 125, 126, 131, 132, 160, 161, 166, 167, 168, 169, 174, 175, 176, 177, 182, 183, 184

Offset

1,2

Comments

What is the limit_{n->infinity} a(n) / (n*log(n)/LambertW(log(n))) ?. - Vaclav Kotesovec, Aug 30 2021

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Vaclav Kotesovec, Plot of a(n) / (n*log(n)/LambertW(log(n))) for n = 1..10000

Formula

G.f.: (1/(1 - x)) * Sum_{k>=1} k^k * x^(k^k)/(1 - x^(k^k)).

Mathematica

Table[Sum[k^k*Floor[n/k^k], {k, 1, n}], {n, 1, 100}] (* Vaclav Kotesovec, Aug 30 2021 *)

Prog

(PARI) a(n) = sum(k=1, n, k^k*(n\k^k));

Crossrefs

Cf. A024916, A062071, A309125, A309126, A309127.

Sequence in context: A080745 A283776 A047476 * A037462 A309125 A037318

Adjacent sequences: A347394 A347395 A347396 * A347398 A347399 A347400

Keyword

nonn

Author

Seiichi Manyama, Aug 30 2021

Status

approved