A345030 a(n) = Sum_{k=1..n} n^(floor(n/k) - 1).

1, 3, 11, 70, 633, 7821, 117709, 2097684, 43047545, 1000010125, 25937439391, 743008621422, 23298085496173, 793714780786669, 29192926036832363, 1152921504875352376, 48661191876077295937, 2185911559749718388655, 104127350297928227579629

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..387

Formula

a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} x^k * (1 - x^k)/(1 - n*x^k).

a(n) ~ n^(n-1). - Vaclav Kotesovec, Jan 29 2026

Mathematica

a[n_] := Sum[n^(Floor[n/k] - 1), {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Jun 06 2021 *)

Prog

(PARI) a(n) = sum(k=1, n, n^(n\k-1));
(Python)
def A345030(n):
    c, j = 0, 1
    while j <= n:
        c += n**((k:=n//j)-1)*(-j+(j:=n//k+1))
    return c # Chai Wah Wu, Jan 28 2026

Crossrefs

Diagonal of A345032.

Cf. A023037, A332533, A344551, A345036.

Sequence in context: A009103 A018192 A056665 * A378047 A127716 A035378

Adjacent sequences: A345027 A345028 A345029 * A345031 A345032 A345033

Keyword

nonn

Author

Seiichi Manyama, Jun 06 2021

Status

approved