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Number of divisors d|n such that neither d nor n/d is a perfect power greater than 1.
2

%I #12 Aug 18 2020 07:23:36

%S 1,2,2,1,2,4,2,0,1,4,2,4,2,4,4,0,2,4,2,4,4,4,2,4,1,4,0,4,2,8,2,0,4,4,

%T 4,5,2,4,4,4,2,8,2,4,4,4,2,4,1,4,4,4,2,4,4,4,4,4,2,10,2,4,4,0,4,8,2,4,

%U 4,8,2,6,2,4,4,4,4,8,2,4,0,4,2,10,4,4,4,4

%N Number of divisors d|n such that neither d nor n/d is a perfect power greater than 1.

%H Antti Karttunen, <a href="/A304649/b304649.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%e The a(36) = 5 ways to write 36 as a product of two numbers that are not perfect powers greater than 1 are 2*18, 3*12, 6*6, 12*3, 18*2.

%t nn=1000;

%t sradQ[n_]:=GCD@@FactorInteger[n][[All,2]]===1;

%t Table[Length@Select[Divisors[n],sradQ[n/#]&&sradQ[#]&],{n,nn}]

%o (PARI) a(n) = sumdiv(n, d, !ispower(d) && !ispower(n/d)); \\ _Michel Marcus_, May 17 2018

%Y Cf. A000005, A001055, A007427, A007916, A034444, A045778, A162247, A183096, A281116, A301700, A303386, A303707, A304650.

%K nonn

%O 1,2

%A _Gus Wiseman_, May 15 2018