A355196 Sum of the largest parts of the partitions of n into exactly 3 prime parts.

0, 0, 0, 0, 0, 0, 2, 3, 3, 8, 5, 12, 12, 12, 7, 23, 18, 38, 24, 31, 24, 59, 30, 73, 47, 71, 49, 113, 55, 115, 40, 102, 59, 171, 48, 168, 100, 191, 102, 220, 50, 265, 89, 246, 120, 322, 109, 383, 136, 348, 181, 477, 158, 516, 117, 468, 199, 605, 133, 574, 170, 600, 252, 751, 133

Offset

0,7

Links

Table of n, a(n) for n=0..64.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} c(i) * c(j) * c(n-i-j) * (n-i-j), where c = A010051.

a(n) = A355199(n) - A355197(n) - A355198(n).

Example

a(9) = 8; since 9 can be written as the sum of 3 primes in two ways: 2+2+5 = 3+3+3 and the sum of the largest parts of these partitions is 5+3 = 8, we have a(9) = 8.

Mathematica

Table[Sum[Sum[(n - i - j) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[j] - PrimePi[j - 1]) (PrimePi[n - i - j] - PrimePi[n - i - j - 1]), {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 0, 80}]

Crossrefs

Cf. A010051, A068307, A355197, A355198, A355199.

Sequence in context: A347823 A185297 A329803 * A202818 A256679 A193997

Adjacent sequences: A355193 A355194 A355195 * A355197 A355198 A355199

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 23 2022

Status

approved