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A341882
Number of ordered factorizations of n into 6 factors > 1.
3
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6
OFFSET
64,33
LINKS
Eric Weisstein's World of Mathematics, Ordered Factorization
FORMULA
Dirichlet g.f.: (zeta(s) - 1)^6.
a(n) = 15 * A000005(n) - 20 * A007425(n) + 15 * A007426(n) - 6 * A061200(n) + A034695(n) - 6 for n > 1.
MAPLE
b:= proc(n) option remember; series(x*(1+add(b(n/d),
d=numtheory[divisors](n) minus {1, n})), x, 7)
end:
a:= n-> coeff(b(n), x, 6):
seq(a(n), n=64..160); # Alois P. Heinz, Feb 22 2021
MATHEMATICA
b[n_] := b[n] = Series[x*(1 + Sum[b[n/d],
{d, Divisors[n]~Complement~{1, n}}]), {x, 0, 7}];
a[n_] := Coefficient[b[n], x, 6];
Table[a[n], {n, 64, 160}] (* Jean-François Alcover, Feb 28 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 22 2021
STATUS
approved