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 A284639 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. 16
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS a(1)=infinity is not an integer so is necessarily omitted from the data. LINKS Vincenzo Librandi, Table of n, a(n) for n = 2..1000 EXAMPLE 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. MATHEMATICA 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}] CROSSREFS Cf. A001055, A001597, A007916, A089723. Sequence in context: A203531 A324885 A046645 * A320887 A295923 A325806 Adjacent sequences: A284636 A284637 A284638 * A284640 A284641 A284642 KEYWORD nonn AUTHOR Gus Wiseman, Mar 30 2017 STATUS approved

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Last modified March 25 04:11 EDT 2023. Contains 361511 sequences. (Running on oeis4.)