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%I #13 Apr 06 2017 21:47:59
%S 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,
%T 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,
%U 4,2,5,1,16,1,2,4,4,2,5,1,12,8,2,1,11,2
%N 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.
%C a(1)=infinity is not an integer so is necessarily omitted from the data.
%H Vincenzo Librandi, <a href="/A284639/b284639.txt">Table of n, a(n) for n = 2..1000</a>
%e The a(64)=17 ways to write 64 as a power of a product:
%e (2*2*2*2*2*2)^1 (2*2*2)^2 (2*2)^3 (2)^6
%e (2*2*2*2*4)^1 (2*4)^2 (4)^3
%e (2*2*2*8)^1 (8)^2
%e (2*2*4*4)^1
%e (2*2*16)^1
%e (2*4*8)^1
%e (2*32)^1
%e (4*4*4)^1
%e (4*16)^1
%e (8*8)^1
%e (64)^1.
%t nn=85;
%t postfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[postfacs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t Table[DivisorSum[GCD@@FactorInteger[n][[All,2]],Length[postfacs[n^(1/#)]]&],{n,2,nn}]
%Y Cf. A001055, A001597, A007916, A089723.
%K nonn
%O 2,3
%A _Gus Wiseman_, Mar 30 2017
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