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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
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
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
Sequence in context: A246199 A147276 A219022 * A287298 A117246 A352518
KEYWORD
nonn
AUTHOR
Antonio Roldán, Jul 14 2011
STATUS
approved