A294111 - OEIS

%I #15 Feb 05 2023 15:07:35

%S 0,0,1,3,2,4,2,4,6,8,4,6,8,11,6,8,10,13,16,20,24,28,20,24,28,32,22,25,

%T 28,32,36,41,46,51,38,42,46,51,36,40,44,49,54,60,66,72,54,60,66,72,78,

%U 84,90,97,104,111,118,125,102,109,116,124,100,107,114

%N Sum of the smaller parts of the partitions of n into two parts with larger 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)} i * c(n - i), where c is the prime characteristic (A010051).

%t Table[Sum[i (PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[n/2]}], {n, 80}]

%t Table[Total[Select[IntegerPartitions[n,{2}],PrimeQ[#[[1]]]&][[All,2]]],{n,70}] (* _Harvey P. Dale_, Feb 05 2023 *)

%Y Cf. A010051, A294109.

%K nonn,easy

%O 1,4

%A _Wesley Ivan Hurt_, Oct 22 2017