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A319269 Number of uniform factorizations of n into factors > 1, where a factorization is uniform if all factors appear with the same multiplicity. 1
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, 7, 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, 8, 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)} A045778(n^(1/d)).

EXAMPLE

The a(144) = 17 factorizations:

  (144),

  (2*72), (3*48), (4*36), (6*24), (8*18), (9*16), (12*12),

  (2*3*24), (2*4*18), (2*6*12), (2*8*9), (3*4*12), (3*6*8),

  (2*2*6*6), (2*3*4*6), (3*3*4*4).

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], SameQ@@Length/@Split[#]&]], {n, 100}]

CROSSREFS

Cf. A001055, A045778, A047966, A052409, A072774, A296132, A303386, A317710, A317712, A317717, A317718.

Sequence in context: A086436 A001222 A257091 * A320888 A296132 A253557

Adjacent sequences:  A319266 A319267 A319268 * A319270 A319271 A319272

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 16 2018

STATUS

approved

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Last modified January 19 17:45 EST 2019. Contains 319309 sequences. (Running on oeis4.)