A163368 a(n) = phi(sigma(tau(n))).

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, 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, 4, 6, 8, 2, 12, 2, 6, 4, 4, 6, 8, 2, 6, 2, 6, 2, 12, 6

Offset: 1

Author

Jaroslav Krizek, Jul 25 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A000010, A000040, A000203, A006881, A053287, A062069, A062401, A120944.

Programs

Magma

[EulerPhi(SumOfDivisors(NumberOfDivisors(n))): n in [1..80]]; // Vincenzo Librandi, Dec 21 2016

Maple

with(numtheory): A163368:=n->phi(sigma(tau(n))): seq(A163368(n), n=1..150); # Wesley Ivan Hurt, Dec 19 2016

Mathematica

Table[EulerPhi[DivisorSigma[1, DivisorSigma[0, n]]], {n, 100}] (* G. C. Greubel, Dec 19 2016 *)

PARI

vector(50, n, eulerphi(sigma(numdiv(n)))) \\ G. C. Greubel, Dec 19 2016

Formula

a(n) = A000010(A000203(A000005(n))) = A000010(A062069(n)) = A062401(A000005(n)).

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).