A009223 a(n) = gcd(sigma(n), phi(n)).

1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 4, 2, 6, 8, 1, 2, 3, 2, 2, 4, 2, 2, 4, 1, 6, 2, 4, 2, 8, 2, 1, 4, 2, 24, 1, 2, 6, 8, 2, 2, 12, 2, 4, 6, 2, 2, 4, 3, 1, 8, 2, 2, 6, 8, 24, 4, 2, 2, 8, 2, 6, 4, 1, 12, 4, 2, 2, 4, 24, 2, 3, 2, 6, 4, 4, 12, 24, 2, 2, 1, 2, 2, 8, 4, 6, 8, 20, 2, 6, 8, 4, 4, 2, 24, 4, 2, 3, 12, 1, 2, 8

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

The asymptotic density of numbers k such that a(k) <= m for a given m is 0 (Dressler, 1974). - Amiram Eldar, Mar 02 2021

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Robert E. Dressler, On a theorem of Niven, Canadian Mathematical Bulletin, Vol. 17, No. 1 (1974), pp. 109-110.

Crossrefs

Cf. A000010 (phi), A000203 (sigma).

Programs

Haskell

a009223 n = gcd (a000203 n) (a000010 n)
-- Reinhard Zumkeller, Jan 19 2014

Mathematica

Table[GCD[DivisorSigma[1,n],EulerPhi[n]],{n,110}] (* Harvey P. Dale, Aug 10 2011 *)

PARI

a(n)=gcd(sigma(n=factor(n)), eulerphi(n)) \\ Charles R Greathouse IV, Nov 27 2013

Formula

a(n) = gcd(A000203(n), A000010(n)).