A344245 - OEIS

%I #8 May 21 2021 16:49:08

%S 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,

%T 19,19,23,26,28,27,27,32,36,37,39,42,45,44,51,55,58,55,57,66,71,75,76,

%U 82,84,87,93,104,103,103,105,119,131,130,134,141,145,151,163,173,176,173

%N Number of partitions of n into 5 semiprime parts.

%H Alois P. Heinz, <a href="/A344245/b344245.txt">Table of n, a(n) for n = 20..10000</a>

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

%F 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.

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

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

%Y Cf. A340756.

%Y Column k=5 of A344447.

%K nonn

%O 20,7

%A _Wesley Ivan Hurt_, May 12 2021