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a(n) = Sum_{prime p <= n} n!/p.
7

%I #9 Sep 03 2017 03:30:08

%S 1,5,20,124,744,5928,47424,426816,4268160,50578560,606942720,

%T 8369256960,117169597440,1757543961600,28120703385600,498974747443200,

%U 8981545453977600,177051737331302400,3541034746626048000

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

%H Harvey P. Dale, <a href="/A110373/b110373.txt">Table of n, a(n) for n = 2..449</a>

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

%p 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

%t Table[n! Total[1/Prime[Range[PrimePi[n]]]],{n,20}] (* _Harvey P. Dale_, Mar 06 2017 *)

%Y Cf. A110374.

%K easy,nonn

%O 2,2

%A _Amarnath Murthy_, Jul 24 2005

%E More terms from _Emeric Deutsch_, Jul 24 2005