OFFSET
1,4
COMMENTS
Also the number of uniform multiset partitions of the multiset of prime indices of n, where a multiset partition is uniform if all parts have the same size.
LINKS
EXAMPLE
The a(1260) = 13 factorizations:
(1260) (18*70) (4*9*35) (2*2*3*3*5*7)
(20*63) (6*6*35)
(28*45) (4*15*21)
(30*42) (6*10*21)
(12*105) (6*14*15)
(9*10*14)
The a(1260) = 13 multiset partitions:
{{1},{1},{2},{2},{3},{4}}
{{1,1},{2,2},{3,4}}
{{1,1},{2,3},{2,4}}
{{1,2},{1,2},{3,4}}
{{1,2},{1,3},{2,4}}
{{1,2},{1,4},{2,3}}
{{2,2},{1,3},{1,4}}
{{1,1,2},{2,3,4}}
{{1,2,2},{1,3,4}}
{{1,1,3},{2,2,4}}
{{1,1,4},{2,2,3}}
{{1,2,3},{1,2,4}}
{{1,1,2,2,3,4}}
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@@PrimeOmega/@#&]], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 26 2018
STATUS
approved