A386402 a(n) = denominator(sigma(n)*phi(n)/n^2).

1, 4, 9, 8, 25, 3, 49, 16, 27, 25, 121, 9, 169, 49, 75, 32, 289, 18, 361, 25, 147, 121, 529, 6, 125, 169, 81, 7, 841, 25, 961, 64, 363, 289, 1225, 108, 1369, 361, 507, 10, 1681, 49, 1849, 121, 225, 529, 2209, 36, 343, 125, 289, 169, 2809, 27, 605, 49, 361, 841, 3481, 75

Offset: 1

Author

Stefano Spezia, Jul 20 2025

Keywords

• nonn
• easy
• frac

Comments

A386401(n)/a(n) = sigma(n)*phi(n)/n^2 is a multiplicative function since it is the product of three multiplicative functions.

References

• James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, Exercise 5.3.21 on page 169.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A000203, A000290.

Cf. A386401 (numerators).

Programs

Mathematica

a[n_]:=Denominator[DivisorSigma[1,n]EulerPhi[n]/n^2]; Array[a,60]

PARI

a(n) = {my(f = factor(n)); denominator(sigma(f) * eulerphi(f) / n^2);} \\ Amiram Eldar, Jul 21 2025