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A327399 Number of factorizations of n that are constant or whose distinct factors are pairwise coprime. 3
1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 3, 2, 2, 2, 3, 1, 5, 1, 2, 2, 2, 2, 6, 1, 2, 2, 3, 1, 5, 1, 3, 3, 2, 1, 4, 2, 3, 2, 3, 1, 3, 2, 3, 2, 2, 1, 7, 1, 2, 3, 4, 2, 5, 1, 3, 2, 5, 1, 5, 1, 2, 3, 3, 2, 5, 1, 4, 3, 2, 1, 7, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

First differs from A327400 at A327400(24) = 4, a(24) = 3.

LINKS

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

Gus Wiseman, Sequences counting and encoding certain classes of multisets

FORMULA

a(n) = A327695(n) + A089723(n).

EXAMPLE

The a(90) = 7 factorizations together with the corresponding multiset partitions of {1,2,2,3}:

  (2*3*3*5)  {{1},{2},{2},{3}}

  (2*5*9)    {{1},{3},{2,2}}

  (2*45)     {{1},{2,2,3}}

  (3*3*10)   {{2},{2},{1,3}}

  (5*18)     {{3},{1,2,2}}

  (9*10)     {{2,2},{1,3}}

  (90)       {{1,2,2,3}}

MATHEMATICA

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

Table[Length[Select[facs[n], Length[Union[#]]==1||CoprimeQ@@Union[#]&]], {n, 100}]

CROSSREFS

Constant factorizations are A089723.

Partitions whose distinct parts are pairwise coprime are A304709.

Factorizations that are constant or relatively prime are A327400.

See link for additional cross-references.

A007359, A050320, A051424, A281116, A302569, A302696, A304711.

Sequence in context: A076755 A317751 A106490 * A122375 A038548 A320732

Adjacent sequences:  A327396 A327397 A327398 * A327400 A327401 A327402

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 22 2019

STATUS

approved

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Last modified May 18 18:33 EDT 2021. Contains 343998 sequences. (Running on oeis4.)