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A327400 Number of factorizations of n that are constant or whose factors are relatively prime. 3
1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 2, 3, 1, 5, 1, 2, 2, 2, 2, 7, 1, 2, 2, 4, 1, 5, 1, 3, 3, 2, 1, 6, 2, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 9, 1, 2, 3, 4, 2, 5, 1, 3, 2, 5, 1, 10, 1, 2, 3, 3, 2, 5, 1, 6, 3, 2, 1, 9, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

First differs from A327399 at a(24) = 4, A327399(24) = 3.

LINKS

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

FORMULA

a(n) = A281116(n) + A089723(n).

EXAMPLE

The factorizations of 2, 4, 12, 24, 30, 36, 48, and 60 that are constant or whose factors are relatively prime:

  2   4     12      24        30      36        48          60

      2*2   3*4     3*8       5*6     4*9       3*16        3*20

            2*2*3   2*3*4     2*15    6*6       2*3*8       4*15

                    2*2*2*3   3*10    2*2*9     3*4*4       5*12

                              2*3*5   2*3*6     2*2*3*4     2*5*6

                                      3*3*4     2*2*2*2*3   3*4*5

                                      2*2*3*3               2*2*15

                                                            2*3*10

                                                            2*2*3*5

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||GCD@@#==1&]], {n, 100}]

CROSSREFS

Constant factorizations are A089723.

Cf. A007359, A051424, A281116, A302569, A304709, A304711, A319269, A327399.

Sequence in context: A320732 A305149 A336737 * A323303 A068108 A342679

Adjacent sequences:  A327397 A327398 A327399 * A327401 A327402 A327403

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 22 2019

STATUS

approved

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Last modified July 31 23:46 EDT 2021. Contains 346377 sequences. (Running on oeis4.)