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A193003 Squares k such that gcd(sigma(k),usigma(k)) > 1, where usigma is A034448. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A027470

Adjacent sequences:  A193000 A193001 A193002 * A193004 A193005 A193006

KEYWORD

nonn

AUTHOR

Antonio Roldán, Jul 14 2011

STATUS

approved

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Last modified September 17 21:46 EDT 2021. Contains 347489 sequences. (Running on oeis4.)