A239282 a(n) = A045917(n)*prime(n).

0, 3, 5, 7, 22, 13, 34, 38, 46, 58, 93, 111, 123, 86, 141, 106, 236, 244, 134, 213, 292, 237, 332, 445, 388, 303, 515, 321, 436, 678, 381, 655, 822, 278, 745, 906, 785, 815, 1169, 692, 895, 1448, 955, 772, 1773, 796, 1055, 1561, 681, 1374, 1864, 1195, 1446, 2008

Offset: 1

Author

Raghavendra Ugare, Mar 14 2014

Keywords

• nonn

Crossrefs

Cf. A045917, A000040

Programs

Mathematica

(*Returns the various ways a number (presumed to be even) can be split as a sum of 2 Primes.*)
getGoldBachSplits[n_Integer] := Module[{i, splits = {}, a, b},
  (
   For[i = 1,
    Prime[i] < n,
    i++,
    a = Prime[i] ;
    b = n - Prime[i];
    If[PrimeQ[b],
     If[MemberQ[splits, {b, a}], Null,
      AppendTo[splits, {a, b}]],
     Null];
    ]; (*End For-loop...*)
   splits
   )
  ]
(* Now we generate our series...*)
series[n_] :=
Module[{}, (Table[Prime[i]*Length[getGoldBachSplits[2 i]], {i, 2, n}])]