The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A299764

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A299764

Number of special products of factorizations of n into factors > 1.
(history; published version)

#16 by Susanna Cuyler at Sun Jun 10 21:15:55 EDT 2018

STATUS

proposed

approved

#15 by Gus Wiseman at Sun Jun 10 08:36:34 EDT 2018

STATUS

editing

proposed

#14 by Gus Wiseman at Sun Jun 10 08:36:21 EDT 2018

CROSSREFS

Cf. A000712, A001055, A003963, A122768, A292886, A299701, A301829, A301830, A301854, A301957, A301979, A304796.

#13 by Gus Wiseman at Sun Jun 10 08:20:41 EDT 2018

EXAMPLE

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).

#12 by Gus Wiseman at Sun Jun 10 08:12:53 EDT 2018

NAME

Number of special products of factorizations of n into factors greater than one> 1.

CROSSREFS

Cf. A000712, A001055, A003963, A122768, A292886, A299701, A301829, A301830, A301854, A301957, A301979, A304796.

#11 by Gus Wiseman at Fri Jun 08 03:35:25 EDT 2018

NAME

allocated for Gus WisemanNumber of special products of factorizations of n into factors greater than one.

DATA

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

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.

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).

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. A000712, A003963, A122768, A292886, A299701, A301829, A301830, A301854, A301957, A301979, A304796.

KEYWORD

allocated

nonn

AUTHOR

Gus Wiseman, Jun 08 2018

STATUS

approved

editing

#10 by Gus Wiseman at Fri Jun 08 03:35:25 EDT 2018

NAME

allocated for Gus Wiseman

KEYWORD

recycled

allocated

#9 by N. J. A. Sloane at Thu Jun 07 21:58:19 EDT 2018

STATUS

reviewed

approved

#8 by Bruno Berselli at Thu Jun 07 11:18:31 EDT 2018

STATUS

proposed

reviewed

#7 by Michel Marcus at Thu Jun 07 10:39:16 EDT 2018

STATUS

editing

proposed