A110373 a(n) = Sum_{prime p <= n} n!/p.

1, 5, 20, 124, 744, 5928, 47424, 426816, 4268160, 50578560, 606942720, 8369256960, 117169597440, 1757543961600, 28120703385600, 498974747443200, 8981545453977600, 177051737331302400, 3541034746626048000

Offset: 2

Author

Amarnath Murthy, Jul 24 2005

Keywords

• easy
• nonn

Examples

			a(7) = 7!(1/2 + 1/3 + 1/5 + 1/7) = 5928.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 2..449

Crossrefs

Cf. A110374.

Programs

Maple

a:=proc(n) local s, i: s:=0: for i from 2 to n do if isprime(i)=true then s:=s+1/i else s:=s: fi: od: n!*s: end: seq(a(n),n=2..23); # Emeric Deutsch, Jul 24 2005

Mathematica

Table[n! Total[1/Prime[Range[PrimePi[n]]]],{n,20}] (* Harvey P. Dale, Mar 06 2017 *)

Extensions

More terms from Emeric Deutsch, Jul 24 2005