A356238 a(n) = Sum_{k=1..n} (k * floor(n/k))^n.

1, 8, 62, 849, 8541, 206345, 2581403, 76623522, 1617299079, 49463993875, 952905453423, 59000021366675, 1198427462876421, 54128102218676115, 2321105129608323165, 117387839988330848902, 3205342976298888473968, 268263812478494295219717

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..386

Formula

a(n) = Sum_{k=1..n} k^n * Sum_{d|k} (1 - (1 - 1/d)^n).

Mathematica

a[n_] := Sum[(k * Floor[n/k])^n, {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Jul 30 2022 *)

Prog

(PARI) a(n) = sum(k=1, n, (k*(n\k))^n);
(PARI) a(n) = sum(k=1, n, k^n*sumdiv(k, d, 1-(1-1/d)^n));
(Python)
from sympy import bernoulli
def A356238(n):
    c, j = 0, 1
    while j <= n:
        k = n//j
        m = n//k
        c += k**n*(bernoulli(n+1, m+1)-bernoulli(n+1, j))
        j = m+1
    return c//(n+1) # Chai Wah Wu, May 14 2026

Crossrefs

Cf. A007778, A350109, A350125, A356239, A356240.

Sequence in context: A356461 A099335 A377349 * A374421 A194930 A346625

Adjacent sequences: A356235 A356236 A356237 * A356239 A356240 A356241

Keyword

nonn

Author

Seiichi Manyama, Jul 30 2022

Status

approved