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A284639
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Number of ways to write n > 1 as a power of a product n = (x_1*..*x_k)^y, where y >= 1, x_i > 1, and x_i <= x_j for i < j.
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16
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1, 1, 3, 1, 2, 1, 4, 3, 2, 1, 4, 1, 2, 2, 8, 1, 4, 1, 4, 2, 2, 1, 7, 3, 2, 4, 4, 1, 5, 1, 8, 2, 2, 2, 11, 1, 2, 2, 7, 1, 5, 1, 4, 4, 2, 1, 12, 3, 4, 2, 4, 1, 7, 2, 7, 2, 2, 1, 11, 1, 2, 4, 17, 2, 5, 1, 4, 2, 5, 1, 16, 1, 2, 4, 4, 2, 5, 1, 12, 8, 2, 1, 11, 2
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OFFSET
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2,3
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COMMENTS
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a(1)=infinity is not an integer so is necessarily omitted from the data.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 2..1000
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EXAMPLE
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The a(64)=17 ways to write 64 as a power of a product:
(2*2*2*2*2*2)^1 (2*2*2)^2 (2*2)^3 (2)^6
(2*2*2*2*4)^1 (2*4)^2 (4)^3
(2*2*2*8)^1 (8)^2
(2*2*4*4)^1
(2*2*16)^1
(2*4*8)^1
(2*32)^1
(4*4*4)^1
(4*16)^1
(8*8)^1
(64)^1.
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MATHEMATICA
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nn=85;
postfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[postfacs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Table[DivisorSum[GCD@@FactorInteger[n][[All, 2]], Length[postfacs[n^(1/#)]]&], {n, 2, nn}]
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CROSSREFS
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Cf. A001055, A001597, A007916, A089723.
Sequence in context: A203531 A324885 A046645 * A320887 A295923 A325806
Adjacent sequences: A284636 A284637 A284638 * A284640 A284641 A284642
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Mar 30 2017
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STATUS
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approved
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