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

1,1

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

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 *)

Prog

(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

Crossrefs

Cf. A000203, A000010, A051612, A065387.

Sequence in context: A240128 A125829 A294647 * A276337 A160385 A076881

Adjacent sequences: A077096 A077097 A077098 * A077100 A077101 A077102

Keyword

nonn

Author

Labos Elemer, Nov 06 2002

Extensions

Edited by Dean Hickerson, Nov 07 2002

Status

approved