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A062513 Product of unitary divisors of n is divided by n^(number of distinct prime factors).

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%I A062513 #8 May 20 2017 14:27:22
%S A062513 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,30,1,1,1,1,
%T A062513 1,1,1,1,1,1,1,42,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,60,1,1,1,1,1,66,1,
%U A062513 1,1,70,1,1,1,1,1,1,1,78,1,1,1,1,1,84,1,1,1,1,1,90,1,1,1,1,1,1,1,1,1,1
%N A062513 Product of unitary divisors of n is divided by n^(number of distinct prime factors).
%H A062513 G. C. Greubel, <a href="/A062513/b062513.txt">Table of n, a(n) for n = 1..5000</a>
%F A062513 a(n) = A061537(n)/[n^A001221(n)].
%F A062513 a(n) = n^[(A034444(n)/2)-A001221(n)].
%e A062513 n=210, with 4 p-divisors; all its 16 divisors are unitary; product=210^(16/2)=3782285936100000000, while 210^4=1944810000; a(210)=3782285936100000000/1944810000=1944810000.
%t A062513 Table[n^(2^(PrimeNu[n] - 1) - PrimeNu[n]), {n,1,50}] (* _G. C. Greubel_, May 20 2017 *)
%o A062513 (PARI) for(n=1,50, print1(round(n^(2^(omega(n) -1) - omega(n))), ", ")) \\ _G. C. Greubel_, May 20 2017
%Y A062513 Cf. A000005, A034444, A001221.
%K A062513 nonn
%O A062513 1,30
%A A062513 _Labos Elemer_, Jul 13 2001