A248695 Decimal expansion of Sum_{n >= 1} n!/p(n), where p(n) = [n/2]!*[n/3]!*...*[n/n]!, and [ ] = floor.

2, 9, 2, 4, 9, 9, 2, 7, 8, 7, 4, 3, 1, 2, 8, 5, 5, 1, 4, 5, 0, 0, 1, 5, 6, 0, 9, 4, 1, 7, 4, 4, 2, 4, 0, 1, 3, 2, 8, 9, 9, 8, 3, 9, 3, 1, 0, 2, 2, 9, 3, 1, 2, 1, 8, 0, 5, 0, 9, 4, 1, 3, 2, 9, 6, 8, 6, 9, 2, 5, 8, 8, 3, 7, 3, 3, 9, 2, 4, 9, 3, 5, 3, 5, 4, 7

Offset: 6

Author

Clark Kimberling, Oct 13 2014

Keywords

• nonn
• easy
• cons

Comments

Let t(n) = n!/p(n). Then t(n) is an integer for n = 1..15, and max{t(n), n = 1..infinity} = t(23) = 77462.802... . It appears that t(n) < 1/10 for n > 35 and t(n) < 10^(-6) for n > 45.

Examples

			292499.27874312855145001560941744240132899839310229312180509413296869258837339...
		

Crossrefs

Cf. A214869, A248696.

Programs

Maple

evalf(sum(n!/product(floor(n/k)!, k=2..n), n=1..infinity), 120); # Vaclav Kotesovec, Oct 19 2014

Mathematica

u = N[Sum[n!/Product[Floor[n/k]!, {k, 2, n}], {n, 1, 200}], 130]
RealDigits[u]  (* A248695 *)

Extensions

Name corrected by Jason Yuen, Feb 27 2025