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A342458 a(n) = gcd(A001615(n), A003415(n)), where A001615 is Dedekind psi, and A003415 is the arithmetic derivative of n.

%I A342458 #13 Mar 29 2021 15:04:53
%S A342458 1,1,1,2,1,1,1,12,6,1,1,8,1,3,8,8,1,3,1,12,2,1,1,4,10,3,9,16,1,1,1,16,
%T A342458 2,1,12,12,1,3,8,4,1,1,1,24,3,1,1,16,14,45,4,28,1,27,8,4,2,1,1,4,1,3,
%U A342458 3,96,6,1,1,36,2,1,1,12,1,3,5,40,6,1,1,16,108,1,1,4,2,3,8,4,1,3,4,48,2,1,24,16,1,7,3,20
%N A342458 a(n) = gcd(A001615(n), A003415(n)), where A001615 is Dedekind psi, and A003415 is the arithmetic derivative of n.
%H A342458 Antti Karttunen, <a href="/A342458/b342458.txt">Table of n, a(n) for n = 1..16384</a>
%F A342458 a(n) = gcd(A001615(n), A003415(n)).
%F A342458 a(n) = A003557(n) * A342459(n).
%F A342458 a(n) = A003415(n) / A342919(n).
%o A342458 (PARI)
%o A342458 A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
%o A342458 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A342458 A342458(n) = gcd(A001615(n), A003415(n));
%Y A342458 Cf. A001615, A003415, A003557, A342459, A342919.
%Y A342458 Cf. A301939 (gives the positions at which a(n) = A001615(n) = A003415(n)).
%Y A342458 Cf. also A175732, A342413, A342915.
%K A342458 nonn
%O A342458 1,4
%A A342458 _Antti Karttunen_, Mar 28 2021