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A341881 Number of ordered factorizations of n into 5 factors > 1. 2
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET

32,17

LINKS

Table of n, a(n) for n=32..128.

Eric Weisstein's World of Mathematics, Ordered Factorization

FORMULA

Dirichlet g.f.: (zeta(s) - 1)^5.

a(n) = -10 * A000005(n) + 10 * A007425(n) - 5 * A007426(n) + A061200(n) + 5 for n > 1.

MAPLE

b:= proc(n) option remember; series(x*(1+add(b(n/d),

      d=numtheory[divisors](n) minus {1, n})), x, 6)

    end:

a:= n-> coeff(b(n), x, 5):

seq(a(n), n=32..128);  # Alois P. Heinz, Feb 22 2021

CROSSREFS

Column k=5 of A251683.

Cf. A000005, A007425, A007426, A061200, A070824, A074206, A200221, A341880, A341882.

Sequence in context: A241471 A152623 A020761 * A281462 A236239 A047752

Adjacent sequences:  A341878 A341879 A341880 * A341882 A341883 A341884

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 22 2021

STATUS

approved

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Last modified April 19 16:51 EDT 2021. Contains 343116 sequences. (Running on oeis4.)