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A320888 Number of set multipartitions (multisets of sets) of factorizations of n into factors > 1 such that all the parts have the same product. 3
1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, 2, 2, 1, 5, 2, 2, 3, 3, 1, 5, 1, 4, 2, 2, 2, 8, 1, 2, 2, 5, 1, 5, 1, 3, 3, 2, 1, 7, 2, 3, 2, 3, 1, 5, 2, 5, 2, 2, 1, 9, 1, 2, 3, 9, 2, 5, 1, 3, 2, 5, 1, 9, 1, 2, 3, 3, 2, 5, 1, 7, 4, 2, 1, 9, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

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

FORMULA

a(n) = Sum_{d|A052409(n)} binomial(A045778(n^(1/d)) + d - 1, d).

EXAMPLE

The a(144) = 20 set multipartitions:

  (2*3*4*6)    (2*8*9)     (2*72)     (144)

  (2*6)*(2*6)  (3*6*8)     (3*48)

  (2*6)*(3*4)  (2*3*24)    (4*36)

  (3*4)*(3*4)  (2*4*18)    (6*24)

               (2*6*12)    (8*18)

               (3*4*12)    (9*16)

               (12)*(2*6)  (12)*(12)

               (12)*(3*4)

MATHEMATICA

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

Table[With[{g=GCD@@FactorInteger[n][[All, 2]]}, Sum[Binomial[Length[strfacs[n^(1/d)]]+d-1, d], {d, Divisors[g]}]], {n, 100}]

CROSSREFS

Cf. A001055, A001970, A045778, A050336, A052409, A089259, A294786, A296132, A319269, A320886, A320887, A320889.

Sequence in context: A001222 A257091 A319269 * A296132 A253557 A098893

Adjacent sequences:  A320885 A320886 A320887 * A320889 A320890 A320891

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 23 2018

STATUS

approved

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Last modified January 20 21:36 EST 2019. Contains 319336 sequences. (Running on oeis4.)