A355199 Sum of all the parts in the partitions of n into exactly 3 prime parts.

0, 0, 0, 0, 0, 0, 6, 7, 8, 18, 10, 22, 24, 26, 14, 45, 32, 68, 36, 57, 40, 105, 44, 115, 72, 125, 78, 189, 84, 203, 60, 186, 96, 297, 68, 280, 144, 333, 152, 390, 80, 451, 126, 430, 176, 540, 138, 611, 192, 588, 250, 765, 208, 848, 162, 770, 280, 969, 174, 944, 240, 976, 372

Offset

0,7

Links

Table of n, a(n) for n=0..62.

Index entries for sequences related to partitions

Formula

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

a(n) = n * A068307(n) for n > 0.

a(n) = A355196(n) + A355197(n) + A355198(n).

Example

a(9) = 18; since 9 can be written as the sum of 3 primes in two ways: 2+2+5 = 3+3+3 and the sum of all the parts of these partitions is (2+2+5)+(3+3+3) = 18, we have a(9) = 18.

Mathematica

Table[n*Sum[Sum[(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, A355196, A355197, A355198.

Sequence in context: A155150 A078745 A087663 * A358557 A112813 A347808

Adjacent sequences: A355196 A355197 A355198 * A355200 A355201 A355202

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 23 2022

Status

approved