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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.
7
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
OFFSET
1,4
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 16 2018
STATUS
approved