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A082070 Smallest prime that divides phi(n) and sigma(n) = A000203(n), or 1 if phi(n) and sigma(n) are relatively prime. 7
1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 1, 2, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

FORMULA

a(n) = A020639(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[x]; f2[x_] := DivisorSigma[1, 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@ #, DivisorSigma[1, #]} &, 105] (* Michael De Vlieger, Nov 03 2017 *)

PROG

(PARI)

A020639(n) = if(1==n, n, vecmin(factor(n)[, 1]));

A082070(n) = A020639(gcd(eulerphi(n), sigma(n))); \\ Antti Karttunen, Nov 03 2017

CROSSREFS

Cf. A000010, A000203, A009223, A020639.

Cf. also A082064, A082067, A082068, A082069, A082071, A082072.

Sequence in context: A248597 A082071 A082065 * A336648 A082902 A123926

Adjacent sequences:  A082067 A082068 A082069 * A082071 A082072 A082073

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 07 2003

EXTENSIONS

Name edited by Antti Karttunen after an example by N. J. A. Sloane, Nov 04 2017

STATUS

approved

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Last modified September 30 12:46 EDT 2022. Contains 357105 sequences. (Running on oeis4.)