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A342415 a(n) = phi(n) / gcd(phi(n),A003415(n)), where A003415(n) is the arithmetic derivative of n, and phi is Euler totient function.

%I A342415 #11 Mar 12 2021 23:13:41
%S A342415 1,1,2,1,4,2,6,1,1,4,10,1,12,2,1,1,16,2,18,1,6,10,22,2,2,4,2,3,28,8,
%T A342415 30,1,10,16,2,1,36,6,3,4,40,12,42,5,8,22,46,1,3,4,8,3,52,2,5,6,18,28,
%U A342415 58,4,60,10,12,1,8,20,66,4,22,24,70,2,72,12,8,9,10,24,78,2,1,40,82,6,32,14,7,2,88,8,18,11,30
%N A342415 a(n) = phi(n) / gcd(phi(n),A003415(n)), where A003415(n) is the arithmetic derivative of n, and phi is Euler totient function.
%H A342415 Antti Karttunen, <a href="/A342415/b342415.txt">Table of n, a(n) for n = 1..12500</a>
%F A342415 a(n) = A000010(n) / A342413(n) = A000010(n) / gcd(A000010(n),A003415(n)).
%F A342415 a(n) = A173557(n) / A342416(n).
%t A342415 Array[#2/GCD[#1, #2] & @@ {If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &@ Abs[#], EulerPhi[#]} &, 93] (* _Michael De Vlieger_, Mar 11 2021 *)
%o A342415 (PARI)
%o A342415 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A342415 A342415(n) = { my(u=eulerphi(n)); (u/gcd(u,A003415(n))); };
%Y A342415 Cf. A000010, A003415, A173557, A342009 (positions of ones), A342413, A342414, A342416.
%K A342415 nonn
%O A342415 1,3
%A A342415 _Antti Karttunen_, Mar 11 2021