A077099 a(n) = gcd(A051612(n), A065387(n)), where A051612(n) = sigma(n) - phi(n) and A065387(n) = sigma(n) + phi(n).

2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 8, 2, 6, 16, 1, 2, 3, 2, 2, 4, 2, 2, 4, 1, 6, 2, 4, 2, 16, 2, 1, 4, 2, 24, 1, 2, 6, 16, 2, 2, 12, 2, 8, 6, 2, 2, 4, 3, 1, 8, 2, 2, 6, 16, 48, 4, 2, 2, 8, 2, 6, 4, 1, 12, 4, 2, 2, 4, 24, 2, 3, 2, 6, 4, 8, 12, 48, 2, 2, 1, 2, 2, 8, 4, 6, 16, 20, 2, 6, 8, 4, 4, 2, 48, 4, 2, 3

Offset: 1

Author

Labos Elemer, Nov 06 2002

Keywords

• nonn

Comments

If a(n)=1, then n is either square or twice a square.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A000010, A051612, A065387.

Programs

Mathematica

sep[n_]:=Module[{s=DivisorSigma[1,n],e=EulerPhi[n]},GCD[s+e,s-e]]; Array[sep,100] (* Harvey P. Dale, Jun 17 2011 *)

PARI

a(n)=my(f=factor(n),s=sigma(f),p=eulerphi(f)); gcd(2*p,s-p) \\ Charles R Greathouse IV, Jan 02 2014

Extensions

Edited by Dean Hickerson, Nov 07 2002