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a(n) = Product_{d|n} A019565(phi(d)), where phi is Euler totient function A000010.
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%I #7 Feb 25 2020 18:33:55

%S 2,4,6,12,10,36,30,60,90,100,42,540,70,900,210,420,22,8100,66,2100,

%T 3150,1764,330,18900,550,4900,2970,94500,770,44100,2310,4620,6930,484,

%U 11550,4252500,130,4356,16170,115500,182,9922500,546,291060,242550,108900,2730,1455300,8190,302500,858,1131900,1430,8820900,19110

%N a(n) = Product_{d|n} A019565(phi(d)), where phi is Euler totient function A000010.

%H Antti Karttunen, <a href="/A332824/b332824.txt">Table of n, a(n) for n = 1..8192</a>

%F a(n) = Product_{d|n} A332825(d).

%F a(n) = A318834(n) * A332825(n).

%F A048675(a(n)) = n.

%F A097248(a(n)) = A019565(n).

%o (PARI)

%o A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565

%o A332824(n) = { my(m=1); fordiv(n,d,m *= A019565(eulerphi(d))); (m); };

%Y Cf. A000010, A019565, A097248, A318834, A332825, A332826, A332827.

%Y Cf. A048675 (a left inverse).

%K nonn

%O 1,1

%A _Antti Karttunen_, Feb 25 2020