login
a(n) = gcd(sigma(n), phi(n)).
26

%I #21 May 11 2023 13:16:18

%S 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,

%T 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,

%U 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

%N a(n) = gcd(sigma(n), phi(n)).

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

%H Charles R Greathouse IV, <a href="/A009223/b009223.txt">Table of n, a(n) for n = 1..10000</a>

%H Robert E. Dressler, <a href="https://doi.org/10.4153/CMB-1974-019-5">On a theorem of Niven</a>, Canadian Mathematical Bulletin, Vol. 17, No. 1 (1974), pp. 109-110.

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

%t Table[GCD[DivisorSigma[1,n],EulerPhi[n]],{n,110}] (* _Harvey P. Dale_, Aug 10 2011 *)

%o (PARI) a(n)=gcd(sigma(n=factor(n)), eulerphi(n)) \\ _Charles R Greathouse IV_, Nov 27 2013

%o (Haskell)

%o a009223 n = gcd (a000203 n) (a000010 n)

%o -- _Reinhard Zumkeller_, Jan 19 2014

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

%K nonn

%O 1,3

%A _David W. Wilson_