A110374 a(n) = Sum_{composite c <= n} n!/c.

6, 30, 300, 2100, 21840, 236880, 2731680, 30048480, 400498560, 5206481280, 79117758720, 1273944672000, 21690789120000, 368743415040000, 6993068898816000, 132868309077504000, 2779011281958912000, 60792138929313792000, 1388517998616612864000

Offset: 4

Author

Amarnath Murthy, Jul 24 2005

Keywords

• easy
• nonn

Examples

			a(8) = 8! * (1/4 + 1/6 + 1/8) = 21840.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 4..449

Crossrefs

Cf. A110373.

Programs

Maple

a:=proc(n) local s,i :s:=0: for i from 4 to n do if isprime(i)=false then s:=s+1/i else s:=s: fi od: n!*s; end; seq(a(n),n=4..23); # Emeric Deutsch, Jul 24 2005

Python

from sympy import factorial, isprime, Rational
def a(n): return factorial(n) * sum(Rational(1, c) for c in range(4, n+1) if not isprime(c))
print([a(n) for n in range(4, 23)]) # Michael S. Branicky, Jun 30 2021

Extensions

More terms from Emeric Deutsch, Jul 24 2005

a(21) and beyond from Michael S. Branicky, Jun 30 2021