OFFSET
0,2
COMMENTS
Number of factorizations of (p*q*r*s*t)^n into distinct factors where p, q, r, s, t are distinct primes.
FORMULA
a(n) = [(v*w*x*y*z)^n] 1/2 * Product_{h,i,j,k,m>=0} (1+v^h*w^i*x^j*y^k*z^m).
MATHEMATICA
a[n_] := a[n] = If[n == 0, 1, (1/2) Coefficient[Product[O[v]^(n+1) + O[w]^(n+1) + O[x]^(n+1) + O[y]^(n+1) + O[z]^(n+1) + (1 + v^i w^j x^k y^l z^m), {i, 0, n}, {j, 0, n}, {k, 0, n}, {l, 0, n}, {m, 0, n}] // Normal, (v w x y z)^n]];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 7}] (* Jean-François Alcover, Sep 24 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 23 2012
EXTENSIONS
a(6) from Alois P. Heinz, Sep 25 2014
a(7)-a(15) from Andrew Howroyd, Dec 16 2018
STATUS
approved