A344255 - OEIS

%I #7 May 21 2021 16:45:12

%S 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,

%T 29,33,36,44,45,51,54,59,63,71,78,87,90,99,106,120,124,136,147,157,

%U 166,182,199,216,223,238,259,280,298,314

%N Number of partitions of n into 8 semiprime parts.

%H Alois P. Heinz, <a href="/A344255/b344255.txt">Table of n, a(n) for n = 32..10000</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F 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.

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

%Y Cf. A001222 (Omega), A001358.

%Y Column k=8 of A344447.

%K nonn

%O 32,7

%A _Wesley Ivan Hurt_, May 12 2021