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A342414 a(n) = A003415(n) / gcd(phi(n),A003415(n)), where A003415(n) is the arithmetic derivative of n, and phi is Euler totient function.

%I A342414 #12 Mar 12 2021 23:13:31
%S A342414 0,1,1,2,1,5,1,3,1,7,1,4,1,3,1,4,1,7,1,3,5,13,1,11,1,5,3,8,1,31,1,5,7,
%T A342414 19,1,5,1,7,2,17,1,41,1,12,13,25,1,7,1,9,5,7,1,9,2,23,11,31,1,23,1,11,
%U A342414 17,6,3,61,1,9,13,59,1,13,1,13,11,20,3,71,1,11,2,43,1,31,11,15,4,7,1,41,5,24,17,49,1,17
%N A342414 a(n) = A003415(n) / gcd(phi(n),A003415(n)), where A003415(n) is the arithmetic derivative of n, and phi is Euler totient function.
%H A342414 Antti Karttunen, <a href="/A342414/b342414.txt">Table of n, a(n) for n = 1..12500</a>
%H A342414 Antti Karttunen, <a href="/A342414/a342414.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A342414 a(n) = A003415(n) / A342413(n) = A003415(n) / gcd(A000010(n),A003415(n)).
%F A342414 a(n) = A342001(n) / A342416(n).
%t A342414 Array[#1/GCD[#1, #2] & @@ {If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &@ Abs[#], EulerPhi[#]} &, 96] (* _Michael De Vlieger_, Mar 11 2021 *)
%o A342414 (PARI)
%o A342414 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A342414 A342414(n) = { my(u=A003415(n)); (u/gcd(eulerphi(n),u)); };
%Y A342414 Cf. A000010, A003415, A342001, A342008 (positions of ones), A342413, A342415, A342416.
%K A342414 nonn
%O A342414 1,4
%A A342414 _Antti Karttunen_, Mar 11 2021