|
%I #7 Jun 15 2020 23:35:31
%S 0,0,4,10,23,33,39,68,76,85,116,138,175,228,242,257,306,375,393,470,
%T 490,511,578,624,697,773,799,881,966,1024,1054,1179,1276,1309,1412,
%U 1447,1483,1632,1747,1786,1907,1989,2116,2289,2333,2469,2608,2797,2845,2993,3043
%N Sum of the largest composite parts in the partitions of 2n into two parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{i=1..n} (2*n-i) * (1 - c(2*n-i)) * (1 - [2*n-i = 1]), where [] is the Iverson bracket and c is the prime characteristic (A010051).
%e a(5) = 23; 2*5 = 10 has 3 partitions into two parts with largest part composite, (9,1), (8,2) and (6,4). The sum is then 9 + 8 + 6 = 23.
%t Table[Sum[(2 n - i) (1 - PrimePi[2 n - i] + PrimePi[2 n - i - 1]) (1 - KroneckerDelta[2 n - i, 1]), {i, n}], {n, 80}]
%Y Cf. A010051.
%K nonn,easy
%O 1,3
%A _Wesley Ivan Hurt_, Apr 20 2020
|
