A273160 a(n) = Sum_{k=1..n} C(n, floor((n-k)/k)).

0, 1, 3, 5, 10, 13, 30, 39, 84, 143, 290, 424, 1120, 1697, 3521, 6633, 14012, 22721, 53529, 88607, 189749, 356024, 730697, 1256272, 2889484, 5006918, 10399649, 19706342, 40954970, 72663140, 160499071, 286286349, 597385864, 1134282375, 2340807724, 4251969339

Offset

0,3

Links

Table of n, a(n) for n=0..35.

Formula

a(n) ~ 2^(n + 1/2) / sqrt(Pi*n). - Vaclav Kotesovec, May 28 2021

Maple

A273160:=n->add(binomial(n, floor((n-i)/i)), i=1..n): seq(A273160(n), n=0..50);

Mathematica

Table[Sum[Binomial[n, Floor[(n - i)/i]], {i, n}], {n, 0, 40}]

Prog

(Python)
from math import comb
def A273160(n):
    c, j = 0, 1
    while j <= n:
        c += comb(n, (k:=n//j)-1)*(-j+(j:=n//k+1))
    return c # Chai Wah Wu, Jan 28 2026

Crossrefs

Cf. A051054, A273161.

Sequence in context: A137395 A001767 A360956 * A285138 A310018 A048214

Adjacent sequences: A273157 A273158 A273159 * A273161 A273162 A273163

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 16 2016

Status

approved