A344255 Number of partitions of n into 8 semiprime parts.

1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 4, 3, 5, 3, 5, 5, 8, 8, 9, 8, 12, 12, 17, 16, 18, 18, 22, 25, 30, 29, 33, 36, 44, 45, 51, 54, 59, 63, 71, 78, 87, 90, 99, 106, 120, 124, 136, 147, 157, 166, 182, 199, 216, 223, 238, 259, 280, 298, 314

Offset

32,7

Links

Alois P. Heinz, Table of n, a(n) for n = 32..10000

Index entries for sequences related to partitions

Formula

a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} [Omega(p) = Omega(o) = Omega(m) = Omega(l) = Omega(k) = Omega(j) = Omega(i) = Omega(n-i-j-k-l-m-o-p) = 2], where Omega is the number of prime factors with multiplicity (A001222) and [ ] is the (generalized) Iverson bracket.

a(n) = [x^n y^8] 1/Product_{j>=1} (1-y*x^A001358(j)). - Alois P. Heinz, May 21 2021

Crossrefs

Cf. A001222 (Omega), A001358.

Column k=8 of A344447.

Sequence in context: A226279 A344246 A344254 * A344256 A344257 A088931

Adjacent sequences: A344252 A344253 A344254 * A344256 A344257 A344258

Keyword

nonn

Author

Wesley Ivan Hurt, May 12 2021

Status

approved