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A082064
Greatest common prime-divisor of phi(n) and sigma(n) = A000203(n); a(n)=1 if no common prime-divisor exists.
4
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
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
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