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A341880
Number of ordered factorizations of n into 4 factors > 1.
3
1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 12, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 16, 1, 0, 0, 12, 0, 0, 0, 4, 0, 12, 0, 0, 0, 0, 0, 40, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 28, 0, 0, 0, 16
OFFSET
16,9
LINKS
Eric Weisstein's World of Mathematics, Ordered Factorization
FORMULA
Dirichlet g.f.: (zeta(s) - 1)^4.
a(n) = 6 * A000005(n) - 4 * A007425(n) + A007426(n) - 4 for n > 1.
MAPLE
b:= proc(n) option remember; series(x*(1+add(b(n/d),
d=numtheory[divisors](n) minus {1, n})), x, 5)
end:
a:= n-> coeff(b(n), x, 4):
seq(a(n), n=16..112); # 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, 5}];
a[n_] := Coefficient[b[n], x, 4];
Table[a[n], {n, 16, 112}] (* Jean-François Alcover, Feb 28 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 22 2021
STATUS
approved