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A301856 Number of subset-products (greater than 1) of factorizations of n into factors greater than 1. 8
0, 1, 1, 3, 1, 4, 1, 7, 3, 4, 1, 12, 1, 4, 4, 14, 1, 12, 1, 12, 4, 4, 1, 29, 3, 4, 7, 12, 1, 17, 1, 27, 4, 4, 4, 36, 1, 4, 4, 29, 1, 17, 1, 12, 12, 4, 1, 62, 3, 12, 4, 12, 1, 29, 4, 29, 4, 4, 1, 53, 1, 4, 12, 47, 4, 17, 1, 12, 4, 17, 1, 90, 1, 4, 12, 12, 4, 17 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

For a finite multiset p of positive integers greater than 1 with product n, a pair (t > 1, p) is defined to be a subset-product if there exists a nonempty submultiset of p with product t.

LINKS

Table of n, a(n) for n=1..78.

EXAMPLE

The a(12) = 12 subset-products:

12<=(2*2*3), 6<=(2*2*3), 4<=(2*2*3), 3<=(2*2*3), 2<=(2*2*3),

12<=(2*6),   6<=(2*6),   4<=(3*4),   3<=(3*4),   2<=(2*6),

12<=(3*4),

12<=(12).

The a(16) = 14 subset-products:

16<=(16),

16<=(4*4),

16<=(2*8),     8<=(2*8),     4<=(4*4),     2<=(2*8),

16<=(2*2*4),   8<=(2*2*4),   4<=(2*2*4),   2<=(2*2*4),

16<=(2*2*2*2), 8<=(2*2*2*2), 4<=(2*2*2*2), 2<=(2*2*2*2).

MATHEMATICA

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

Table[Sum[Length[Union[Times@@@Rest[Subsets[f]]]], {f, facs[n]}], {n, 100}]

CROSSREFS

Cf. A001055, A000712, A045778, A108917, A162247, A276024, A281116, A284640, A292886, A301829, A301830.

Sequence in context: A094119 A210622 A295276 * A301829 A006022 A078896

Adjacent sequences:  A301853 A301854 A301855 * A301857 A301858 A301859

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 27 2018

STATUS

approved

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Last modified February 18 06:13 EST 2019. Contains 320245 sequences. (Running on oeis4.)