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a(n) = A045917(n)*prime(n).
0

%I #8 Mar 17 2014 02:11:01

%S 0,3,5,7,22,13,34,38,46,58,93,111,123,86,141,106,236,244,134,213,292,

%T 237,332,445,388,303,515,321,436,678,381,655,822,278,745,906,785,815,

%U 1169,692,895,1448,955,772,1773,796,1055,1561,681,1374,1864,1195,1446,2008

%N a(n) = A045917(n)*prime(n).

%t (*Returns the various ways a number (presumed to be even) can be split as a sum of 2 Primes.*)

%t getGoldBachSplits[n_Integer] := Module[{i, splits = {}, a, b},

%t (

%t For[i = 1,

%t Prime[i] < n,

%t i++,

%t a = Prime[i] ;

%t b = n - Prime[i];

%t If[PrimeQ[b],

%t If[MemberQ[splits, {b, a}], Null,

%t AppendTo[splits, {a, b}]],

%t Null];

%t ]; (*End For-loop...*)

%t splits

%t )

%t ]

%t (* Now we generate our series...*)

%t series[n_] :=

%t Module[{}, (Table[Prime[i]*Length[getGoldBachSplits[2 i]], {i, 2, n}])]

%Y Cf. A045917, A000040

%K nonn

%O 1,2

%A _Raghavendra Ugare_, Mar 14 2014