A259196 Number of partitions of n into six primes.

1, 1, 1, 2, 2, 3, 4, 3, 4, 5, 6, 6, 8, 7, 10, 10, 12, 11, 16, 12, 19, 17, 22, 18, 26, 20, 31, 24, 33, 27, 42, 29, 47, 35, 51, 38, 60, 41, 68, 47, 73, 53, 86, 54, 95, 64, 103, 70, 116, 73, 131, 81, 137, 89, 156, 92, 171, 103, 180, 112, 202, 117, 223, 127, 232

Offset

12,4

Links

Alois P. Heinz, Table of n, a(n) for n = 12..10000

Index entries for sequences related to partitions

Formula

a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_(i=j..floor((n-j-k-l-m)/2)} A010051(i) * A010051(j) * A010051(k) * A010051(l) * A010051(m) * A010051(n-i-j-k-l-m). - Wesley Ivan Hurt, Apr 17 2019

a(n) = [x^n y^6] Product_{k>=1} 1/(1 - y*x^prime(k)). - Ilya Gutkovskiy, Apr 18 2019

Example

a(17) = 3 because there are 3 partitions of 17 into six primes: [2,2,2,2,2,7], [2,2,2,3,3,5] and [2,3,3,3,3,3].

Mathematica

Table[Count[IntegerPartitions[n, {6}], _?(AllTrue[#, PrimeQ]&)], {n, 12, 80}] (* Harvey P. Dale, Jul 27 2024 *)

Crossrefs

Column k=6 of A117278.

Number of partitions of n into r primes for r = 1-10: A010051, A061358, A068307, A259194, A259195, this sequence, A259197, A259198, A259200, A259201.

Cf. A000040.

Sequence in context: A356998 A132919 A162619 * A357589 A336200 A032355

Adjacent sequences: A259193 A259194 A259195 * A259197 A259198 A259199

Keyword

nonn,easy

Author

Doug Bell, Jun 20 2015

Status

approved