A344246 Number of partitions of n into 6 semiprime parts.

1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 4, 3, 5, 3, 4, 5, 7, 7, 8, 7, 10, 11, 14, 13, 15, 14, 17, 21, 24, 22, 25, 27, 32, 33, 36, 38, 41, 43, 47, 54, 58, 57, 63, 68, 77, 78, 83, 89, 94, 97, 106, 118, 123, 125, 131, 146, 156, 162, 166, 179, 187, 198, 211, 226, 236, 236, 251, 274, 290, 296

Offset

24,7

Links

Alois P. Heinz, Table of n, a(n) for n = 24..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)} [Omega(m) = Omega(l) = Omega(k) = Omega(j) = Omega(i) = Omega(n-i-j-k-l-m) = 2], where Omega is the number of prime factors with multiplicity (A001222) and [ ] is the (generalized) Iverson bracket.

a(n) = [x^n y^6] 1/Product_{j>=1} (1-y*x^A001358(j)). - Alois P. Heinz, May 21 2021

Crossrefs

Cf. A001222 (Omega), A001358.

Column k=6 of A344447.

Sequence in context: A344245 A308213 A226279 * A344254 A344255 A344256

Adjacent sequences: A344243 A344244 A344245 * A344247 A344248 A344249

Keyword

nonn

Author

Wesley Ivan Hurt, May 12 2021

Status

approved