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%I #15 Sep 17 2020 17:05:51
%S 0,0,0,2,3,7,9,11,13,20,23,26,29,39,43,47,51,55,59,63,67,82,87,92,97,
%T 115,121,127,133,139,145,151,157,180,187,194,201,227,235,243,251,259,
%U 267,275,283,314,323,332,341,350,359,368,377,386,395,404,413,451
%N Sum of the larger parts of the partitions of n into two parts with smaller part prime.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{i=1..floor(n/2)} (n - i) * c(i), where c is the prime characteristic (A010051).
%t Table[Sum[(n - i) (PrimePi[i] - PrimePi[i - 1]), {i, Floor[n/2]}], {n, 80}]
%t Table[Total[Select[IntegerPartitions[n,{2}],PrimeQ[#[[2]]]&][[All,1]]],{n,80}] (* _Harvey P. Dale_, Jul 08 2019 *)
%Y Cf. A010051, A294111.
%K nonn,easy
%O 1,4
%A _Wesley Ivan Hurt_, Oct 22 2017