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%I #25 Jun 23 2019 11:52:20
%S 225,576,900,3600,8649,11025,14400,19881,20449,21025,27225,28224,
%T 34596,38025,44100,47961,53824,57600,58564,62001,65025,69696,79524,
%U 81225,81796,84100,93025,97344,106929,108900,119025,131769,138384,140625,152100,164025,166464
%N Squares k such that gcd(sigma(k),usigma(k)) > 1, where usigma is A034448.
%C For n less than 4*10^6, the only values of G=gcd(sigma(n),usigma(n)) are 5, 13, 37, 61, 65, 73 y 793. In the remaining square numbers G=1.
%C All divisors of G are the form 4n+1.
%H Amiram Eldar, <a href="/A193003/b193003.txt">Table of n, a(n) for n = 1..10000</a>
%H A. Roldan Martinez, <a href="http://hojaynumeros.blogspot.com/2011/07/divisores-unitarios-3-relaciones-entre.html">Numeros y hoja de calculo</a> (Spanish)
%e 38025=3^2*5^2*13^2; sigma(38025)=73749=3*13*31*61; usigma(38025)=44200=2^3*5^2*13*17; GCD=13.
%t usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); Select[Range[408]^2, GCD[DivisorSigma[1, #], usigma[#]] > 1 &] (* _Amiram Eldar_, Jun 23 2019 *)
%o (PARI) usigma(n)= {local(f, u=1); f=factor(n); for(i=1, matsize(f)[1], u*=(1+ f[i, 1]^f[i, 2])); return(u)}
%o { for (n=1, 10^6, if (gcd(sigma(n),usigma(n))>1 && issquare(n), print1(n,", "))); } // _Antonio Roldán_, Oct 05 2012
%Y Cf. A000203, A034448.
%K nonn
%O 1,1
%A _Antonio Roldán_, Jul 14 2011
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