A370690 Denominator of sigma(phi(n))/phi(sigma(n)), where sigma is the sum of the divisors function and phi is the Euler totient function.

1, 2, 2, 2, 2, 4, 1, 8, 1, 6, 2, 12, 3, 2, 8, 2, 6, 2, 8, 4, 4, 2, 2, 16, 5, 3, 16, 6, 1, 8, 2, 36, 8, 18, 4, 18, 18, 16, 2, 24, 2, 8, 5, 4, 2, 2, 2, 60, 3, 10, 8, 7, 9, 32, 4, 8, 32, 3, 8, 48, 5, 4, 48, 2, 6, 8, 2, 4, 8, 4, 1, 8, 12, 36, 2, 48, 4, 4, 4, 20, 11

Offset: 1

Author

Amiram Eldar, Feb 27 2024

Keywords

• nonn
• easy
• frac

Comments

See A370689 for details.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Jean-Marie De Koninck and Florian Luca, On the composition of the Euler function and the sum of divisors function, Colloquium Mathematicum, Vol. 108, No. 1 (2007), pp. 31-51.

Crossrefs

Cf. A000010, A000203, A033632, A062401, A062402, A065395, A066930 (positions of 1's), A073858, A289336, A289412, A370689 (numerators).

Programs

Mathematica

Table[DivisorSigma[1, EulerPhi[n]]/EulerPhi[DivisorSigma[1, n]], {n, 1, 100}] // Denominator

PARI

a(n) = {my(f = factor(n)); denominator(sigma(eulerphi(f)) / eulerphi(sigma(f)));}