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A296118 Number of ways to choose a factorization of each factor in a strict factorization of n. 7
1, 1, 1, 2, 1, 3, 1, 5, 2, 3, 1, 8, 1, 3, 3, 8, 1, 8, 1, 8, 3, 3, 1, 20, 2, 3, 5, 8, 1, 12, 1, 18, 3, 3, 3, 23, 1, 3, 3, 20, 1, 12, 1, 8, 8, 3, 1, 45, 2, 8, 3, 8, 1, 20, 3, 20, 3, 3, 1, 38, 1, 3, 8, 34, 3, 12, 1, 8, 3, 12, 1, 66, 1, 3, 8, 8, 3, 12, 1, 45, 8, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

FORMULA

Dirichlet g.f.: Product_{n > 1}(1 + A001055(n)/n^s).

EXAMPLE

The a(12) = 8 twice-factorizations are (2)*(2*3), (2)*(6), (3)*(2*2), (3)*(4), (2*2*3), (2*6), (3*4), (12).

MATHEMATICA

facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];

Table[Sum[Times@@(Length[facs[#]]&/@f), {f, Select[facs[n], UnsameQ@@#&]}], {n, 100}]

PROG

(PARI)

A001055(n, m=n) = if(1==n, 1, sumdiv(n, d, if((d>1)&&(d<=m), A001055(n/d, d))));

A296118(n, m=n) = ((n<=m)*A001055(n) + sumdiv(n, d, if((d>1)&&(d<=m)&&(d<n), A001055(d)*A296118(n/d, d-1)))); \\ Antti Karttunen, Oct 08 2018

CROSSREFS

Cf. A000009, A005117, A045778, A261049, A271619, A281113, A294788, A295923, A296119, A296121.

Sequence in context: A173284 A278136 A085053 * A296121 A277120 A104725

Adjacent sequences:  A296115 A296116 A296117 * A296119 A296120 A296121

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 05 2017

STATUS

approved

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Last modified November 13 15:41 EST 2019. Contains 329106 sequences. (Running on oeis4.)