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A327522
Number of factorizations of the n-th prime power A000961(n) into prime powers > 1.
0
0, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 7, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1
OFFSET
1,7
FORMULA
a(n) = A000041(A001222(A000961(n))).
EXAMPLE
The a(32) = 5 factorizations of 81:
(3*3*3*3)
(3*3*9)
(3*27)
(9*9)
(81)
The a(32) = 5 multiset partitions of the prime indices of 81 into constant multisets:
{{2},{2},{2},{2}}
{{2},{2},{2,2}}
{{2},{2,2,2}}
{{2,2},{2,2}}
{{2,2,2,2}}
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], PrimePowerQ];
Table[Length[facsusing[Rest[y], n]], {n, y}]
CROSSREFS
See link for additional cross-references.
Sequence in context: A248641 A282934 A273619 * A034003 A376612 A306722
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 15 2019
STATUS
approved