cp's OEIS Frontend

A385122 a(n) = d(phi(n)) - phi(d(n)) where d(n) = A000005(n) is the number of divisors and phi(n) = A000010(n) is the Euler totient function.

%I A385122 #12 Jun 19 2025 11:56:45
%S A385122 0,0,1,0,2,0,3,1,2,1,3,1,5,2,2,0,4,2,5,2,4,2,3,0,4,4,4,4,5,0,7,3,4,3,
%T A385122 6,0,8,4,6,1,7,2,7,4,6,2,3,1,6,4,4,6,5,2,6,4,7,4,3,1,11,6,7,0,8,2,7,4,
%U A385122 4,4,7,4,11,7,6,7,10,4,7,2,4,6,3,4,5,6
%N A385122 a(n) = d(phi(n)) - phi(d(n)) where d(n) = A000005(n) is the number of divisors and phi(n) = A000010(n) is the Euler totient function.
%C A385122 First negative value is a(120) = -2.
%H A385122 Sean A. Irvine, <a href="/A385122/b385122.txt">Table of n, a(n) for n = 1..10000</a>
%F A385122 a(n) = A000005(A000010(n)) - A000010(A000005(n)).
%F A385122 a(n) = A062821(n) - A163109(n).
%t A385122 A385122[n_] := DivisorSigma[0, EulerPhi[n]] - EulerPhi[DivisorSigma[0, n]];
%t A385122 Array[A385122, 100] (* _Paolo Xausa_, Jun 19 2025 *)
%o A385122 (PARI) a(n) = numdiv(eulerphi(n)) - eulerphi(numdiv(n)); \\ _Michel Marcus_, Jun 19 2025
%Y A385122 Cf. A000005, A000010, A062821, A078148, A078150, A163109.
%K A385122 sign
%O A385122 1,5
%A A385122 _Sean A. Irvine_, Jun 18 2025