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

1,6

Links

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

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}]

Prog

(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

Crossrefs

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

Sequence in context: A226166 A209155 A376369 * A030370 A100808 A010277

Adjacent sequences: A082059 A082060 A082061 * A082063 A082064 A082065

Keyword

nonn

Author

Labos Elemer, Apr 07 2003

Extensions

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

Status

approved