A082068 Smallest common prime-divisor of n and sigma(n) = A000203(n); a(n)=1 if no common prime-divisor exists.

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

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = A020639(A009194(n)). - Antti Karttunen, Nov 03 2017

Mathematica

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_] := n; f2[x_] := DivisorSigma[1, x]; Table[Min[Intersection[ba[f1[w]], ba[f2[w]]]], {w, 1, 128}]
(* Second program: *)
Array[If[CoprimeQ[#1, #2], 1, Min@ Apply[Intersection, Map[FactorInteger[#][[All, 1]] &, {#1, #2}]]] & @@ {#, DivisorSigma[1, #]} &, 105] (* Michael De Vlieger, Nov 03 2017 *)

Prog

(PARI)
A020639(n) = if(1==n, n, vecmin(factor(n)[, 1]));
A082068(n) = A020639(gcd(sigma(n), n)); \\ Antti Karttunen, Nov 03 2017

Crossrefs

Cf. A000203, A009194, A020639.

Cf. also A082062, A082067, A082069, A082070, A082071, A082072.

Sequence in context: A303759 A330754 A330753 * A300360 A300396 A300356

Adjacent sequences: A082065 A082066 A082067 * A082069 A082070 A082071

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