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A327524
Number of factorizations of the n-th uniform number A072774(n) into uniform numbers > 1.
2
1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 1, 2, 2, 5, 1, 1, 2, 2, 1, 2, 2, 3, 1, 5, 1, 7, 2, 2, 2, 7, 1, 2, 2, 1, 5, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 11, 2, 5, 1, 2, 5, 1, 1, 2, 2, 5, 1, 5, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 7, 1, 5, 1, 5, 2, 1, 1, 5, 2, 1, 5, 2, 2, 2
OFFSET
1,4
COMMENTS
A number is uniform if its prime multiplicities are all equal, meaning it is a power of a squarefree number. Uniform numbers are listed in A072774.
EXAMPLE
The a(31) = 7 factorizations of 36 into uniform numbers together with the corresponding multiset partitions of {1,1,2,2}:
(2*2*3*3) {{1},{1},{2},{2}}
(2*2*9) {{1},{1},{2,2}}
(2*3*6) {{1},{2},{1,2}}
(3*3*4) {{2},{2},{1,1}}
(4*9) {{1,1},{2,2}}
(6*6) {{1,2},{1,2}}
(36) {{1,1,2,2}}
MATHEMATICA
nn=100;
facsusing[s_, n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facsusing[Select[s, Divisible[n/d, #]&], n/d], Min@@#>=d&]], {d, Select[s, Divisible[n, #]&]}]];
y=Select[Range[nn], SameQ@@Last/@FactorInteger[#]&];
Table[Length[facsusing[Rest[y], n]], {n, y}];
CROSSREFS
See link for additional cross-references.
Sequence in context: A332423 A256106 A077480 * A059829 A363369 A304465
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 17 2019
STATUS
approved