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%I #16 Jan 29 2022 13:12:46
%S 1,1,1,1,1,3,1,1,1,2,1,2,1,2,3,1,1,3,1,2,1,2,1,3,1,2,1,7,1,3,1,1,3,2,
%T 1,1,1,2,1,5,1,3,1,2,3,2,1,2,1,1,3,2,1,3,1,2,1,2,1,3,1,2,1,1,1,3,1,2,
%U 3,2,1,3,1,2,1,2,1,3,1,2,1,2,1,7,1,2,3,2,1,3,7,2,1,2,5,3,1,1,3,1,1,3,1,2,3
%N Greatest common prime-divisor of n and sigma(n)=A000203(n); a(n)=1 if no common prime-divisor exists.
%H Reinhard Zumkeller, <a href="/A082062/b082062.txt">Table of n, a(n) for n = 1..10000</a>
%t "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_] := DivisorSigma[1, x] Table[Max[Intersection[ba[f1[w]], ba[f2[w]]]], {w, 1, 128}]
%o (PARI) gpf(n)=if(n>1,my(f=factor(n)[,1]);f[#f],1)
%o a(n)=gpf(gcd(sigma(n),n)) \\ _Charles R Greathouse IV_, Feb 19 2013
%Y Cf. A009194, A006530, A000203, A082061-A082065; A192795.
%K nonn
%O 1,6
%A _Labos Elemer_, Apr 07 2003
%E Changed "was found" to "exists" in definition. - _N. J. A. Sloane_, Jan 29 2022
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