A355986 a(n) = Sum_{k=1..n} floor(n/k)!.

1, 3, 8, 28, 125, 731, 5052, 40352, 362917, 3628935, 39916936, 479002360, 6227021561, 87178296283, 1307674373184, 20922789928484, 355687428136485, 6402373706091651, 121645100409195652, 2432902008180269688, 51090942171713074013, 1124000727777647602015

Offset

1,2

Links

Table of n, a(n) for n=1..22.

Example

a(6) = 6! + 3! + 2! + 1! + 1! + 1! = 731.

Mathematica

a[n_] := Sum[Floor[n/k]!, {k, 1, n}]; Array[a, 22] (* Amiram Eldar, Jul 22 2022 *)

Prog

(PARI) a(n) = sum(k=1, n, (n\k)!);
(Python)
from sympy import factorial
def A355986(n):
    c, j = 0, 1
    while j <= n:
        c += factorial(k:=n//j)*(-j+(j:=n//k+1))
    return c # Chai Wah Wu, Jan 29 2026

Crossrefs

Cf. A007489, A060832, A081123.

Sequence in context: A347072 A000776 A327030 * A373753 A000239 A268302

Adjacent sequences: A355983 A355984 A355985 * A355987 A355988 A355989

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 22 2022

Status

approved