36,7

Alois P. Heinz, Table of n, a(n) for n = 36..10000

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} [Omega(q) = Omega(p) = Omega(o) = Omega(m) = Omega(l) = Omega(k) = Omega(j) = Omega(i) = Omega(n-i-j-k-l-m-o-p-q) = 2], where Omega is the number of prime factors with multiplicity (A001222) and [ ] is the (generalized) Iverson bracket.

a(n) = [x^n y^9] 1/Product_{j>=1} (1-y*x^A001358(j)). - Alois P. Heinz, May 21 2021

h[n_] := h[n] = If[n == 0, 0, If[PrimeOmega[n] == 2, n, h[n-1]]];

b[n_, i_] := b[n, i] = Series[If[n == 0, 1, If[i < 1, 0, If[i > n, 0, x*b[n-i, h[Min[n-i, i]]]]+b[n, h[i-1]]]], {x, 0, 10}];

a[n_] := SeriesCoefficient[b[n, h[n]], {x, 0, 9}];

Table[a[n], {n, 36, 120}] (* Jean-François Alcover, May 15 2025, after Alois P. Heinz in A344257 *)

Cf. A001222 (Omega), A001358.

Column k=9 of A344447.

Sequence in context: A344246 A344254 A344255 * A344257 A088931 A088980

Adjacent sequences: A344253 A344254 A344255 * A344257 A344258 A344259

Wesley Ivan Hurt, May 13 2021

More terms from Alois P. Heinz, May 18 2021

approved