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%I #14 Sep 08 2022 08:45:46
%S 1,2,2,2,2,6,2,6,2,6,2,4,2,6,6,2,2,4,2,4,6,6,2,8,2,6,6,4,2,8,2,4,6,6,
%T 6,12,2,6,6,8,2,8,2,4,4,6,2,6,2,4,6,4,2,8,6,8,6,6,2,12,2,6,4,4,6,8,2,
%U 4,6,8,2,12,2,6,4,4,6,8,2,6,2,6,2,12,6
%N a(n) = phi(sigma(tau(n))).
%H G. C. Greubel, <a href="/A163368/b163368.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A000010(A000203(A000005(n))) = A000010(A062069(n)) = A062401(A000005(n)).
%F a(1) = 1, a(p) = 2 for p = primes (A000040), a(pq) = 6 for pq = product of two distinct primes (A006881), a(pq...z) = A000010(2^(k+1)-1) = A053287(k+1) for pq...z = product of k (k > 2) distinct primes p,q,...,z (A120944).
%p with(numtheory): A163368:=n->phi(sigma(tau(n))): seq(A163368(n), n=1..150); # _Wesley Ivan Hurt_, Dec 19 2016
%t Table[EulerPhi[DivisorSigma[1, DivisorSigma[0, n]]], {n, 100}] (* _G. C. Greubel_, Dec 19 2016 *)
%o (PARI) vector(50, n, eulerphi(sigma(numdiv(n)))) \\ _G. C. Greubel_, Dec 19 2016
%o (Magma) [EulerPhi(SumOfDivisors(NumberOfDivisors(n))): n in [1..80]]; // _Vincenzo Librandi_, Dec 21 2016
%Y Cf. A000005, A000010, A000040, A000203, A006881, A053287, A062069, A062401, A120944.
%K nonn,easy
%O 1,2
%A _Jaroslav Krizek_, Jul 25 2009
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