A355198 - OEIS

A355198

Sum of the smallest parts of the partitions of n into exactly 3 prime parts.

0, 0, 0, 0, 0, 0, 2, 2, 2, 5, 2, 5, 4, 6, 2, 10, 4, 13, 4, 11, 4, 20, 4, 18, 6, 21, 6, 28, 6, 31, 4, 30, 6, 46, 4, 41, 8, 49, 8, 58, 4, 64, 6, 64, 8, 73, 6, 80, 8, 80, 10, 98, 8, 114, 6, 106, 10, 124, 6, 124, 8, 124, 12, 136, 6, 172, 10, 164, 12, 170, 4, 193, 10, 183, 12, 189

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OFFSET

0,7

LINKS

Table of n, a(n) for n=0..75.

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) * j, where c = A010051.

a(n) = A355199(n) - A355196(n) - A355197(n).

EXAMPLE

a(9) = 5; 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 smallest parts of these partitions is 2+3 = 5, we have a(9) = 5.

MATHEMATICA

Table[Sum[Sum[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, A355196, A355197, A355199.

Sequence in context: A368302 A368308 A080348 * A363924 A029662 A077913

Adjacent sequences: A355195 A355196 A355197 * A355199 A355200 A355201

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jun 23 2022

STATUS

approved