cp's OEIS Frontend

A342413 a(n) = gcd(phi(n), A003415(n)), where A003415(n) is the arithmetic derivative of n, and phi is Euler totient function.

%I A342413 #17 Mar 12 2021 23:13:04
%S A342413 1,1,1,2,1,1,1,4,6,1,1,4,1,3,8,8,1,3,1,8,2,1,1,4,10,3,9,4,1,1,1,16,2,
%T A342413 1,12,12,1,3,8,4,1,1,1,4,3,1,1,16,14,5,4,8,1,9,8,4,2,1,1,4,1,3,3,32,6,
%U A342413 1,1,8,2,1,1,12,1,3,5,4,6,1,1,16,54,1,1,4,2,3,8,20,1,3,4,4,2,1,24,16,1,7,15,20
%N A342413 a(n) = gcd(phi(n), A003415(n)), where A003415(n) is the arithmetic derivative of n, and phi is Euler totient function.
%H A342413 Antti Karttunen, <a href="/A342413/b342413.txt">Table of n, a(n) for n = 1..12500</a>
%H A342413 Antti Karttunen, <a href="/A342413/a342413.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A342413 a(n) = gcd(A000010(n), A003415(n)).
%F A342413 a(n) = A003415(n) / A342414(n) = A000010(n) / A342415(n).
%F A342413 a(n) = A003557(n) * A342416(n).
%t A342413 Array[GCD[If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]], EulerPhi[#]] &@ Abs[#] &, 100] (* _Michael De Vlieger_, Mar 11 2021 *)
%o A342413 (PARI)
%o A342413 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A342413 A342413(n) = gcd(eulerphi(n), A003415(n));
%Y A342413 Cf. A000010, A003415, A003557, A166374, A342009, A342414, A342415, A342416.
%Y A342413 Cf. also A009195, A085731.
%K A342413 nonn
%O A342413 1,4
%A A342413 _Antti Karttunen_, Mar 11 2021