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%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
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