A193003 Squares k such that gcd(sigma(k),usigma(k)) > 1, where usigma is A034448.

225, 576, 900, 3600, 8649, 11025, 14400, 19881, 20449, 21025, 27225, 28224, 34596, 38025, 44100, 47961, 53824, 57600, 58564, 62001, 65025, 69696, 79524, 81225, 81796, 84100, 93025, 97344, 106929, 108900, 119025, 131769, 138384, 140625, 152100, 164025, 166464

Offset

1,1

Comments

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.

All divisors of G are the form 4n+1.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

A. Roldan Martinez, Numeros y hoja de calculo (Spanish)

Example

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.

Mathematica

usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); Select[Range[408]^2, GCD[DivisorSigma[1, #], usigma[#]] > 1 &] (* Amiram Eldar, Jun 23 2019 *)

Prog

(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)}
{  for (n=1, 10^6, if (gcd(sigma(n), usigma(n))>1 && issquare(n), print1(n, ", "))); } // Antonio Roldán, Oct 05 2012

Crossrefs

Cf. A000203, A034448.

Sequence in context: A246199 A147276 A219022 * A287298 A117246 A352518

Adjacent sequences: A193000 A193001 A193002 * A193004 A193005 A193006

Keyword

nonn

Author

Antonio Roldán, Jul 14 2011

Status

approved