A060832 a(n) = Sum_{k>0} floor(n/k!).

0, 1, 3, 4, 6, 7, 10, 11, 13, 14, 16, 17, 20, 21, 23, 24, 26, 27, 30, 31, 33, 34, 36, 37, 41, 42, 44, 45, 47, 48, 51, 52, 54, 55, 57, 58, 61, 62, 64, 65, 67, 68, 71, 72, 74, 75, 77, 78, 82, 83, 85, 86, 88, 89, 92, 93, 95, 96, 98, 99, 102, 103, 105, 106, 108, 109, 112, 113

Offset: 0

Author

Henry Bottomley, May 01 2001

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A013936, A013939, A038663, A055881.

Programs

Magma

[0] cat [&+[Floor(m/Factorial(k)):k in [1..m]]:m in [1..70]]; // Marius A. Burtea, Jul 11 2019

PARI

a(n)={my(s=0, d=1, f=1); while (n>=d, s+=n\d; f++; d*=f); s} \\ Harry J. Smith, Jul 12 2009

PARI

a(n) = round(sumpos(k=1, n\k!)); \\ Michel Marcus, Jan 24 2025

Formula

a(n) = a(n-1) + A055881(n).

a(n) = (e-1)*n + f(n) where f(n) < 0. - Benoit Cloitre, Jun 19 2002

f is unbounded in the negative direction. The assertion that f(n) < 0 is correct, since (e-1)*n = Sum_{k>=1} n/k! is term for term >= this sequence. - Franklin T. Adams-Watters, Nov 03 2005

G.f.: (1/(1 - x)) * Sum_{k>=1} x^(k!)/(1 - x^(k!)). - Ilya Gutkovskiy, Jul 11 2019