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A320889 Number of set partitions of strict factorizations of n into factors > 1 such that all the blocks have the same product. 3
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, 6, 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, 5, 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

LINKS

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

EXAMPLE

The a(144) = 17 set partitions:

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

  (2*6)*(3*4)  (3*6*8)     (3*48)

               (2*3*24)    (4*36)

               (2*4*18)    (6*24)

               (2*6*12)    (8*18)

               (3*4*12)    (9*16)

               (2*6)*(12)

               (3*4)*(12)

MATHEMATICA

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

sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];

Table[Length[Join@@Table[Select[sps[fac], SameQ@@Times@@@#&], {fac, strfacs[n]}]], {n, 100}]

CROSSREFS

Cf. A000110, A001055, A001970, A045778, A050336, A279375, A294786, A294787, A296132, A320886, A320887, A320888.

Sequence in context: A318357 A323091 A045778 * A296133 A033103 A245661

Adjacent sequences:  A320886 A320887 A320888 * A320890 A320891 A320892

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 23 2018

STATUS

approved

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Last modified April 24 22:26 EDT 2019. Contains 322446 sequences. (Running on oeis4.)