A082062 Greatest common prime-divisor of n and sigma(n)=A000203(n); a(n)=1 if no common prime-divisor exists.

1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 7, 1, 3, 1, 1, 3, 2, 1, 1, 1, 2, 1, 5, 1, 3, 1, 2, 3, 2, 1, 2, 1, 1, 3, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 1, 3, 1, 2, 3, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 7, 1, 2, 3, 2, 1, 3, 7, 2, 1, 2, 5, 3, 1, 1, 3, 1, 1, 3, 1, 2, 3

Offset: 1

Author

Labos Elemer, Apr 07 2003

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A009194, A006530, A000203, A082061-A082065; A192795.

Programs

Mathematica

"factors/exponent SET "; ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] f1[x_] := x; f2[x_] := DivisorSigma[1, x] Table[Max[Intersection[ba[f1[w]], ba[f2[w]]]], {w, 1, 128}]

PARI

gpf(n)=if(n>1,my(f=factor(n)[,1]);f[#f],1)
a(n)=gpf(gcd(sigma(n),n)) \\ Charles R Greathouse IV, Feb 19 2013

Extensions

Changed "was found" to "exists" in definition. - N. J. A. Sloane, Jan 29 2022