%I #13 Mar 29 2021 15:04:53

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

%H Antti Karttunen, <a href="/A342458/b342458.txt">Table of n, a(n) for n = 1..16384</a>

%F a(n) = gcd(A001615(n), A003415(n)).

%F a(n) = A003557(n) * A342459(n).

%F a(n) = A003415(n) / A342919(n).

%o (PARI)

%o 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 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A342458(n) = gcd(A001615(n), A003415(n));

%Y Cf. A001615, A003415, A003557, A342459, A342919.

%Y Cf. A301939 (gives the positions at which a(n) = A001615(n) = A003415(n)).

%Y Cf. also A175732, A342413, A342915.

%K nonn

%O 1,4

%A _Antti Karttunen_, Mar 28 2021