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%I A290479 #7 Aug 06 2018 22:39:47
%S A290479 1,1,1,1,1,6,1,1,1,10,1,6,1,14,15,1,1,6,1,10,21,22,1,6,1,26,1,14,1,
%T A290479 27000,1,1,33,34,35,6,1,38,39,10,1,74088,1,22,15,46,1,6,1,10,51,26,1,
%U A290479 6,55,14,57,58,1,27000,1,62,21,1,65,287496,1,34,69,343000,1,6,1,74,15,38,77,474552,1,10
%N A290479 Product of nonprime squarefree divisors of n.
%H A290479 Antti Karttunen, <a href="/A290479/b290479.txt">Table of n, a(n) for n = 1..65537</a>
%F A290479 a(n) = A078599(n)/A007947(n).
%F A290479 a(n) = rad(n)^(d(rad(n))/2-1), where d() is the number of divisors of n (A000005) and rad() is the squarefree kernel of n (A007947).
%F A290479 a(n) = 1 if n is a prime power.
%e A290479 a(30) = 27000 because 30 has 8 divisors {1, 2, 3, 5, 6, 10, 15, 30} among which 5 are nonprime squarefree {1, 6, 10, 15, 30} and 1*6*10*15*30 = 27000.
%t A290479 Table[Product[d, {d, Select[Divisors[n], !PrimeQ[#] && SquareFreeQ[#] &]}], {n, 80}]
%t A290479 Table[Last[Select[Divisors[n], SquareFreeQ]]^(DivisorSigma[0, Last[Select[Divisors[n], SquareFreeQ]]]/2 - 1), {n, 80}]
%o A290479 (PARI) A290479(n) = if(1==n, n, my(r=factorback(factorint(n)[, 1])); (r^((numdiv(r)/2)-1))); \\ _Antti Karttunen_, Aug 06 2018
%Y A290479 Cf. A000005, A000469, A006881 (fixed points), A007947, A007955, A007956, A061537, A062758, A078599, A087652, A126192, A136655, A183091, A284118.
%K A290479 nonn
%O A290479 1,6
%A A290479 _Ilya Gutkovskiy_, Aug 03 2017

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