A082067 Smallest prime that divides n and phi(n)=A000010(n), or 1 if n and phi(n) are relatively prime.

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

Offset

1,4

Links

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

Formula

a(n) = A020639(A009195(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_] := EulerPhi[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}]]] & @@ {#, EulerPhi@ #} &, 105] (* Michael De Vlieger, Nov 03 2017 *)

Prog

(PARI)
A020639(n) = if(1==n, n, vecmin(factor(n)[, 1]));
A082067(n) = A020639(gcd(eulerphi(n), n)); \\ Antti Karttunen, Nov 03 2017

Crossrefs

Cf. A000010, A009195.

Cf. also A082061, A082068, A082069, A082070, A082071, A082072.

Sequence in context: A094076 A089611 A248470 * A082061 A327979 A107286

Adjacent sequences: A082064 A082065 A082066 * A082068 A082069 A082070

Keyword

nonn

Author

Labos Elemer, Apr 07 2003

Extensions

Name clarified by Antti Karttunen, Nov 03 2017

Status

approved