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A082066 Greatest common prime-divisor of sigma_1(n)=A000203(n) and sigma_2(n)=A001157(n); a(n)=1 if no common prime-divisor was found. 4
1, 1, 2, 7, 2, 2, 2, 5, 13, 2, 2, 7, 2, 2, 2, 31, 2, 13, 2, 7, 2, 2, 2, 5, 31, 2, 5, 7, 2, 2, 2, 7, 2, 2, 2, 13, 2, 5, 2, 5, 2, 2, 2, 7, 13, 2, 2, 31, 19, 31, 2, 7, 2, 5, 2, 5, 5, 5, 2, 7, 2, 2, 13, 127, 2, 2, 2, 7, 2, 2, 2, 13, 2, 2, 31, 7, 2, 2, 2, 31, 11, 2, 2, 7, 2, 2, 5, 5, 2, 13, 2, 7, 2, 2, 2, 7, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A006530(A179931(n)). - Reinhard Zumkeller, Jul 10 2011

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_] := DivisorSigma[1, n]; f2[x_] := DivisorSigma[2, x] Table[Max[Intersection[ba[f1[w]], ba[f2[w]]]], {w, 1, 128}]

(* Second program: *)

Table[Last[Apply[Intersection, FactorInteger[Map[DivisorSigma[#, n] &, {1, 2}]][[All, All, 1]]] /. {} -> {1}], {n, 109}] (* Michael De Vlieger, May 22 2017 *)

PROG

(PARI) gpf(n)=if(n>1, my(f=factor(n)[, 1]); f[#f], 1)

a(n)=gpf(gcd(sigma(n), sigma(n, 2))) \\ Charles R Greathouse IV, Feb 19 2013

(Python)

from sympy import primefactors, gcd, divisor_sigma

def a006530(n): return 1 if n==1 else primefactors(n)[-1]

def a(n): return a006530(gcd(divisor_sigma(n), divisor_sigma(n, 2))) # Indranil Ghosh, May 22 2017

CROSSREFS

Cf. A006530, A001157, A000203, A082061-A082065.

Sequence in context: A023399 A195476 A082072 * A179931 A130335 A073246

Adjacent sequences:  A082063 A082064 A082065 * A082067 A082068 A082069

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 07 2003

STATUS

approved

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Last modified August 22 11:15 EDT 2017. Contains 290946 sequences.