A082069 Smallest common prime-divisor of n and Sigma_2(n) = A001157(n); a(n) = 1 if no common prime-divisor exists.

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

Offset

1,6

Links

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

Formula

a(n) = A020639(A179930(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[2, 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[2, #]} &, 105] (* Michael De Vlieger, Nov 03 2017 *)

Prog

(PARI)
A020639(n) = if(1==n, n, vecmin(factor(n)[, 1]));
A082069(n) = A020639(gcd(sigma(n, 2), n)); \\ Antti Karttunen, Nov 03 2017

Crossrefs

Cf. A001157, A020639, A179930.

Cf. also A082063, A082067, A082068, A082070, A082071, A082072.

Sequence in context: A300360 A300396 A300356 * A136755 A156775 A064693

Adjacent sequences: A082066 A082067 A082068 * A082070 A082071 A082072

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