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a(n) = numerator of the sum of the reciprocals of the n primes from prime(n(n-1)/2+1) to prime(n(n+1)/2).
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%I #4 Dec 05 2013 19:56:03

%S 1,8,311,40808,12185065,6287341056,4738802232119,5387114456064096,

%T 8850391860017878609,18339240151336533115830,

%U 44718225006409477834272143,173879507464360746581828003860

%N a(n) = numerator of the sum of the reciprocals of the n primes from prime(n(n-1)/2+1) to prime(n(n+1)/2).

%C Sum of all possible products of taking n-1 primes out of next n primes.

%t a[n_] := Numerator[Sum[1/Prime[i], {i, n(n-1)/2+1, n(n+1)/2}]]

%K nonn

%O 1,2

%A _Amarnath Murthy_, Apr 04 2003

%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 08 2003