A334260 Sum of the largest composite parts in the partitions of 2n into two parts.

0, 0, 4, 10, 23, 33, 39, 68, 76, 85, 116, 138, 175, 228, 242, 257, 306, 375, 393, 470, 490, 511, 578, 624, 697, 773, 799, 881, 966, 1024, 1054, 1179, 1276, 1309, 1412, 1447, 1483, 1632, 1747, 1786, 1907, 1989, 2116, 2289, 2333, 2469, 2608, 2797, 2845, 2993, 3043

Offset

1,3

Links

Table of n, a(n) for n=1..51.

Index entries for sequences related to partitions

Formula

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).

Example

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.

Mathematica

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}]

Crossrefs

Cf. A010051.

Sequence in context: A241430 A023378 A276308 * A038423 A002071 A375749

Adjacent sequences: A334257 A334258 A334259 * A334261 A334262 A334263

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 20 2020

Status

approved