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A323091 Number of strict knapsack factorizations of n. 1
1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 3, 2, 2, 1, 5, 1, 2, 2, 3, 1, 5, 1, 3, 2, 2, 2, 4, 1, 2, 2, 5, 1, 5, 1, 3, 3, 2, 1, 7, 1, 3, 2, 3, 1, 5, 2, 5, 2, 2, 1, 9, 1, 2, 3, 3, 2, 5, 1, 3, 2, 5, 1, 9, 1, 2, 3, 3, 2, 5, 1, 7, 2, 2, 1, 9, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

A strict knapsack factorization is a finite set of positive integers > 1 such that every subset has a different product.

LINKS

Table of n, a(n) for n=1..87.

FORMULA

a(prime^n) = A275972(n).

EXAMPLE

The a(144) = 11 factorizations:

  (144),

  (2*72), (3*48), (4*36),(6*24), (8*18), (9*16),

  (2*3*24), (2*4*18), (2*8*9), (3*6*8).

Missing from this list are (2*6*12), (3*4*12), (2*3*4*6), which are not knapsack.

MATHEMATICA

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

Table[Length[Select[strfacs[n], UnsameQ@@Times@@@Subsets[#]&]], {n, 100}]

CROSSREFS

Cf. A001055, A045778, A108917, A120641, A275972, A292886, A305150, A323087.

Sequence in context: A056924 A316364 A318357 * A045778 A320889 A296133

Adjacent sequences:  A323088 A323089 A323090 * A323092 A323093 A323094

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 04 2019

STATUS

approved

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Last modified March 23 12:43 EDT 2019. Contains 321430 sequences. (Running on oeis4.)