login
A082061
Greatest common prime-divisor of n and phi(n)=A000010(n); a(n)=1 if no common prime-divisor exists.
7
1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 3, 2, 1, 2, 5, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 3, 2, 1, 3, 1, 2, 3, 2, 1, 2, 7, 5, 1, 2, 1, 3, 5, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 5, 2, 1, 3, 1, 2, 3, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 3, 2, 1, 2, 1, 7, 3, 5, 1, 2, 1, 2, 3
OFFSET
1,4
LINKS
FORMULA
a(n) = A006530(A009195(n)). - Antti Karttunen, Nov 03 2017
MAPLE
gcpd := proc(a, b) local g , d ; g := 1 ; for d in numtheory[divisors](a) intersect numtheory[divisors](b) do if isprime(d) then g := max(g, d) ; end if; end do: g ; end proc:
A082061 := proc(n) gcpd( numtheory[phi](n), n) ; end proc: # R. J. Mathar, Jul 09 2011
MATHEMATICA
(* factors/exponent SET *) 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_] := x; f2[x_] := EulerPhi[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@ #} &, 105] (* Michael De Vlieger, Nov 03 2017 *)
PROG
(PARI) gpf(n)=if(n>1, my(f=factor(n)[, 1]); f[#f], 1)
a(n)=gpf(gcd(eulerphi(n), n)) \\ Charles R Greathouse IV, Feb 19 2013
CROSSREFS
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