A344245 Number of partitions of n into 5 semiprime parts.

1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 4, 3, 4, 3, 4, 4, 6, 7, 7, 6, 8, 9, 13, 11, 11, 12, 15, 16, 18, 18, 19, 19, 23, 26, 28, 27, 27, 32, 36, 37, 39, 42, 45, 44, 51, 55, 58, 55, 57, 66, 71, 75, 76, 82, 84, 87, 93, 104, 103, 103, 105, 119, 131, 130, 134, 141, 145, 151, 163, 173, 176, 173

Offset

20,7

Links

Alois P. Heinz, Table of n, a(n) for n = 20..10000

Index entries for sequences related to partitions

Formula

a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-1)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} [Omega(l) = Omega(k) = Omega(j) = Omega(i) = Omega(n-i-j-k-l) = 2], where Omega is the number of prime factors with multiplicity (A001222) and [ ] is the (generalized) Iverson bracket.

a(n) = [x^n y^5] 1/Product_{j>=1} (1-y*x^A001358(j)). - Alois P. Heinz, May 21 2021

Crossrefs

Cf. A001222 (Omega), A001358 (semiprimes).

Cf. A340756.

Column k=5 of A344447.

Sequence in context: A247074 A160595 A105778 * A308213 A226279 A344246

Adjacent sequences: A344242 A344243 A344244 * A344246 A344247 A344248

Keyword

nonn

Author

Wesley Ivan Hurt, May 12 2021

Status

approved