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A077088 a(n) = phi(sigma(n) - phi(n)), where phi is Euler's totient function and sigma is the sum of divisors function, with a(1) = 0.

%I A077088 #22 Mar 04 2018 17:48:24
%S A077088 0,1,1,4,1,4,1,10,6,6,1,8,1,6,8,22,1,20,1,16,8,12,1,24,10,8,10,20,1,
%T A077088 32,1,46,12,18,8,78,1,12,16,36,1,24,1,32,18,20,1,36,8,72,16,36,1,32,
%U A077088 16,32,20,30,1,72,1,20,32,72,12,60,1,46,24,32,1,108,1,24,24,48,12,48,1,60
%N A077088 a(n) = phi(sigma(n) - phi(n)), where phi is Euler's totient function and sigma is the sum of divisors function, with a(1) = 0.
%C A077088 a(p) = 1 for p prime. Otherwise a(n) is even.
%H A077088 Antti Karttunen, <a href="/A077088/b077088.txt">Table of n, a(n) for n = 1..65537</a>
%F A077088 a(1) = 0; and for n > 1, a(n) = A000010(A051612(n)).
%e A077088 a(10) = 6 because sigma(10) = 18 and phi(10) = 4, and so phi(18 - 4) = phi(14) = 6.
%e A077088 a(11) = 1 because sigma(11) = 12 and phi(11) = 10, so phi(12 - 10) = phi(2) = 1.
%e A077088 a(12) = 8 because sigma(12) = 28 and phi(12) = 4, so phi(28 - 4) = phi(24) = 8.
%p A077088 with(numtheory); A077088:=n->phi(sigma(n)-phi(n)); seq(A077088(n), n=1..100); # _Wesley Ivan Hurt_, Dec 02 2013
%t A077088 Table[EulerPhi[DivisorSigma[1, n] - EulerPhi[n]], {n, 100}] (* _Alonso del Arte_, Nov 29 2013 *)
%o A077088 (PARI) A077088(n) = if(1==n,0,eulerphi(sigma(n) - eulerphi(n))); \\ _Antti Karttunen_, Mar 04 2018
%o A077088 (GAP) List([1..100],n->Phi(Sigma(n)-Phi(n))); # _Muniru A Asiru_, Mar 04 2018
%Y A077088 Cf. A000010, A000203, A051612, A065387. See iterations in A077090-A077100.
%K A077088 nonn,easy
%O A077088 1,4
%A A077088 _Labos Elemer_, Nov 04 2002
%E A077088 Value of a(1) clarified by _Antti Karttunen_, Mar 04 2018