A082064 Greatest common prime-divisor of phi(n) and sigma(n) = A000203(n); a(n)=1 if no common prime-divisor exists.

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

Offset

1,3

Links

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

Formula

a(n) = A006530(A009223(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_] := EulerPhi[n]; f2[x_] := DivisorSigma[1, x]; Table[Max[Intersection[ba[f1[w]], ba[f2[w]]]], {w, 1, 128}]
(* Second program: *)
Array[If[CoprimeQ[#1, #2], 1, Max@ Apply[Intersection, Map[FactorInteger[#][[All, 1]] &, {#1, #2}]]] & @@ {EulerPhi@ #, DivisorSigma[1, #]} &, 105] (* Michael De Vlieger, Nov 03 2017 *)

Prog

(PARI)
A006530(n) = if(1==n, n, vecmax(factor(n)[, 1]));
A082064(n) = A006530(gcd(eulerphi(n), sigma(n))); \\ Antti Karttunen, Nov 03 2017

Crossrefs

Cf. A000010, A000203, A006530, A009223.

Cf. also A082061, A082062, A082063, A082065, A082066, A082070.

Sequence in context: A082902 A123926 A336476 * A082055 A073812 A009223

Adjacent sequences: A082061 A082062 A082063 * A082065 A082066 A082067

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