A243128 - OEIS

%I #18 Jun 04 2014 12:37:00

%S 3,15,21,33,35,39,51,57,69,87,93,105,111,123,129,141,159,165,177,183,

%T 195,201,213,219,231,237,249,255,267,273,285,291,303,309,321,327,339,

%U 345,357,381,385,393,399,411,417,429,435,447,453

%N Squarefree numbers k such that 4k <= sum of squarefree divisors of 4k.

%C Odd squarefree numbers n such that sigma(n)/n >= 4/3. - _Charles R Greathouse IV_, May 30 2014

%C Includes all odd squarefree multiples of its terms. The primitive members are 3, 35, 715, 935, 1001, 1045, 1105, 1235, 1265, .... - _Charles R Greathouse IV_, May 30 2014

%H Charles R Greathouse IV, <a href="/A243128/b243128.txt">Table of n, a(n) for n = 1..10000</a>

%e 3 is in this sequence because 3 is squarefree and 4*3 = A048250(4*3) = 12;

%e 21 is in this sequence because 21 is squarefree and 4*21 = 84 < A048250(4*21) = 96.

%t Select[2Range[250] + 1, MoebiusMu[#] != 0 && DivisorSigma[1, #]/# >= 4/3 &] (* _Alonso del Arte_, May 31 2014 *)

%o (PARI) isok(n) = issquarefree(n) && (sumdiv(4*n, d, issquarefree(d)*d) >= 4*n); \\ _Michel Marcus_, May 30 2014

%o (PARI) is(n)=my(f=factor(n)); n%2 && n>1 && vecmax(f[,2])==1 && sigma(f,-1) >= 4/3 \\ _Charles R Greathouse IV_, May 30 2014

%Y Cf. A005117, A048250.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, May 29 2014