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%I #12 Aug 17 2016 13:09:25
%S 0,1,1,1,2,1,1,1,1,1,3,2,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,2,1,1,2,
%T 1,3,1,1,1,1,1,3,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,
%U 1,1,1,1,1,1,1,1,1,1,1,1,1,5,1,1,1,1,1,1,1,1,1,1,1,1
%N Number of ways the perfect power A001597(n) can be written as a^b, with a, b > 1.
%C Run lengths of A072103. Also, the terms a(n) which exceed 1 constitute A175066. - _Andrey Zabolotskiy_, Aug 17 2016
%F a(n) = A000005(A253641(A001597(n))) - 1.
%F a(n) = A175064(n) - 1.
%e a(1)=0 since A001597(1)=1 can be written as a^b for a=1 and any b, but not using a base a > 1.
%e a(2)=a(3)=a(4)=1 since the following terms 4=2^2, 8=2^3 and 9=3^2 can be written as perfect powers in only one way.
%e a(5)=2 since A001597(5)=16=a^b for (a,b)=(2,4) and (4,2).
%o (PARI) for(n=1,9999,(e=ispower(n))&&print1(numdiv(e)-1,","))
%Y Cf. A001597, A072103, A175064, A253641.
%K nonn
%O 1,5
%A _M. F. Hasler_, Jan 25 2015
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