A345029 a(n) = Sum_{k=1..n} 3^(floor(n/k) - 1).

1, 4, 11, 32, 87, 258, 745, 2224, 6605, 19784, 59151, 177438, 531733, 1595104, 4783811, 14351228, 43049043, 129147030, 387427357, 1162281532, 3486804959, 10460413130, 31381119537, 94143358500, 282429716209, 847289143468, 2541866366735, 7625599086782

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..2000

Formula

G.f.: (1/(1 - x)) * Sum_{k>=1} x^k * (1 - x^k)/(1 - 3*x^k).

a(n) ~ 3^(n-1). - Vaclav Kotesovec, Jan 29 2026

Mathematica

a[n_] := Sum[3^(Floor[n/k] - 1), {k, 1, n}]; Array[a, 30] (* Amiram Eldar, Jun 06 2021 *)

Prog

(PARI) a(n) = sum(k=1, n, 3^(n\k-1));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k*(1-x^k)/(1-3*x^k))/(1-x))
(Python)
def A345029(n):
    c, j = 0, 1
    while j <= n:
        c += 3**((k:=n//j)-1)*(-j+(j:=n//k+1))
    return c # Chai Wah Wu, Jan 28 2026

Crossrefs

Column k=3 of A345032.

Cf. A003462, A345035.

Sequence in context: A027153 A319918 A034754 * A268744 A038747 A052545

Adjacent sequences: A345026 A345027 A345028 * A345030 A345031 A345032

Keyword

nonn

Author

Seiichi Manyama, Jun 06 2021

Status

approved