cp's OEIS Frontend

A342919 a(n) = A003415(n) / gcd(A001615(n), A003415(n)), where A001615 is Dedekind psi, and A003415 is the arithmetic derivative of n.

%I A342919 #8 Mar 30 2021 15:18:20
%S A342919 0,1,1,2,1,5,1,1,1,7,1,2,1,3,1,4,1,7,1,2,5,13,1,11,1,5,3,2,1,31,1,5,7,
%T A342919 19,1,5,1,7,2,17,1,41,1,2,13,25,1,7,1,1,5,2,1,3,2,23,11,31,1,23,1,11,
%U A342919 17,2,3,61,1,2,13,59,1,13,1,13,11,2,3,71,1,11,1,43,1,31,11,15,4,35,1,41,5,2,17,49,1,17,1,11,25
%N A342919 a(n) = A003415(n) / gcd(A001615(n), A003415(n)), where A001615 is Dedekind psi, and A003415 is the arithmetic derivative of n.
%H A342919 Antti Karttunen, <a href="/A342919/b342919.txt">Table of n, a(n) for n = 1..16384</a>
%F A342919 a(n) = A003415(n) / A342458(n) = A003415(n) / gcd(A001615(n), A003415(n)).
%F A342919 a(n) = A342001(n) / A342459(n).
%o A342919 (PARI)
%o A342919 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 A342919 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A342919 A342919(n) = { my(u=A003415(n)); (u/gcd(u, A001615(n))); };
%Y A342919 Cf. A001615, A003415, A342001, A342458, A342459.
%Y A342919 Cf. also A342414.
%K A342919 nonn
%O A342919 1,4
%A A342919 _Antti Karttunen_, Mar 29 2021