A299764 - OEIS

A299764

Number of special products of factorizations of n into factors > 1.

1, 2, 2, 5, 2, 6, 2, 10, 5, 6, 2, 16, 2, 6, 6, 18, 2, 16, 2, 16, 6, 6, 2, 36, 5, 6, 10, 16, 2, 22, 2, 32, 6, 6, 6, 44, 2, 6, 6, 36, 2, 22, 2, 16, 16, 6, 2, 72, 5, 16, 6, 16, 2, 36, 6, 36, 6, 6, 2, 64, 2, 6, 16, 51, 6, 22, 2, 16, 6, 22, 2, 104, 2, 6, 16, 16, 6

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OFFSET

1,2

COMMENTS

A special product of a factorization f is a number n > 0 such that exactly one submultiset of f has product n.

LINKS

Table of n, a(n) for n=1..77.

EXAMPLE

The a(12) = 16 special subset-products:

1<=(12), 12<=(12),

1<=(2*6), 2<=(2*6), 6<=(2*6), 12<=(2*6),

1<=(3*4), 3<=(3*4), 4<=(3*4), 12<=(3*4),

1<=(2*2*3), 2<=(2*2*3), 3<=(2*2*3), 4<=(2*2*3), 6<=(2*2*3), 12<=(2*2*3).

The a(16) = 18 special subset-products:

1<=(16), 16<=(16),

1<=(4*4), 4<=(4*4), 16<=(4*4),

1<=(2*8), 2<=(2*8), 8<=(2*8), 16<=(2*8),

1<=(2*2*4), 2<=(2*2*4), 8<=(2*2*4), 16<=(2*2*4),

1<=(2*2*2*2), 2<=(2*2*2*2), 4<=(2*2*2*2), 8<=(2*2*2*2), 16<=(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]]}]];

sppr[y_]:=Join@@Select[GatherBy[Union[Subsets[y]], Times@@#&], Length[#]===1&];

Table[Length[Join@@sppr/@facs[n]], {n, 30}]

CROSSREFS

Cf. A001055, A292886, A299701, A301829, A301830, A301854, A301957, A301979, A304796.

Sequence in context: A011143 A240081 A305791 * A301830 A305799 A294339

Adjacent sequences: A299761 A299762 A299763 * A299765 A299766 A299767

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 08 2018

STATUS

approved