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A353636 Difference between phi(sigma(n)) and phi(n).

%I A353636 #17 May 06 2022 20:26:53
%S A353636 0,1,0,4,-2,2,-2,4,6,2,-6,8,-6,2,0,22,-10,18,-10,4,4,2,-14,8,10,0,-2,
%T A353636 12,-20,16,-14,20,-4,2,-8,60,-18,-2,0,8,-28,20,-22,4,0,2,-30,44,-6,40,
%U A353636 -8,18,-34,14,-16,8,-4,-4,-42,32,-30,2,12,94,-24,28,-34,4,-12,24,-46,72,-36,0,20,12,-28,24,-46,28,56
%N A353636 Difference between phi(sigma(n)) and phi(n).
%H A353636 Antti Karttunen, <a href="/A353636/b353636.txt">Table of n, a(n) for n = 1..10000</a>
%H A353636 Antti Karttunen, <a href="/A353636/a353636.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A353636 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A353636 a(n) = A062401(n) - A000010(n) = A000010(A000203(n)) - A000010(n).
%F A353636 a(n) = Sum_{d|n} (A353647(d) - A007431(d)).
%t A353636 a[n_] := EulerPhi[DivisorSigma[1, n]] - EulerPhi[n]; Array[a, 100] (* _Amiram Eldar_, May 06 2022 *)
%o A353636 (PARI) A353636(n) = (eulerphi(sigma(n))-eulerphi(n));
%Y A353636 Cf. A000010, A000203, A007431, A062401, A353643, A353647.
%Y A353636 Cf. A006872 (positions of zeros), A353637 (their characteristic function).
%Y A353636 Cf. A353682 (positions of terms >= 0), A353683 (of terms > 0), A353685 (of terms <= 0), A353686 (of negative terms).
%Y A353636 Cf. also A351445.
%K A353636 sign,easy
%O A353636 1,4
%A A353636 _Antti Karttunen_, May 04 2022