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A322794 Number of factorizations of n into factors > 1 where all factors have the same number of prime factors counted with multiplicity. 15
1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 1, 3, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 4, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 3, 2, 3, 2, 2, 1, 4, 1, 2, 2, 4, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 3, 2, 1, 4, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A082477 A036430 A323305 * A163377 A290085 A322867
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 26 2018
STATUS
approved

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Last modified March 29 09:14 EDT 2024. Contains 371268 sequences. (Running on oeis4.)