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A175069 a(n) = product of perfect divisors of n / n.

%I A175069 #11 Nov 21 2017 21:34:43
%S A175069 1,1,1,2,1,1,1,2,3,1,1,1,1,1,1,8,1,1,1,1,1,1,1,1,5,1,3,1,1,1,1,2,1,1,
%T A175069 1,6,1,1,1,1,1,1,1,1,1,1,1,1,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,64,1,1,1,1,
%U A175069 1,1,1,1,1,1,1,1,1,1,1,1,27,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,10
%N A175069 a(n) = product of perfect divisors of n / n.
%C A175069 A perfect divisor of n is a divisor d such that d^k = n for some k >= 1.
%H A175069 Antti Karttunen, <a href="/A175069/b175069.txt">Table of n, a(n) for n = 1..16384</a>
%F A175069 a(n) = A175068(n) / n. a(n) > 1 for perfect powers n = A001597(m) for m > 2.
%t A175069 Table[Apply[Times, Select[Divisors@ n, Or[# == 1, #^IntegerExponent[n, #] == n] &]]/n, {n, 105}] (* _Michael De Vlieger_, Nov 21 2017 *)
%o A175069 (PARI)
%o A175069 A175068(n) = { my(m=1); fordiv(n,d,if((1==d)||(d^valuation(n,d))==n,m*=d)); (m); };
%o A175069 A175069(n) = (A175068(n)/n); \\ _Antti Karttunen_, Nov 21 2017
%Y A175069 Cf. A175068.
%K A175069 nonn
%O A175069 1,4
%A A175069 _Jaroslav Krizek_, Jan 23 2010