A270667 - OEIS

%I #13 Apr 02 2020 03:01:58

%S 1,21,39,57,91,93,111,129,133,183,201,217,219,237,247,259,273,291,301,

%T 309,327,381,399,403,417,427,453,469,471,481,489,511,543,553,559,579,

%U 589,597,633,651,669,679,687,703,721,723,741,763,777,793,813,817,831,849,871,889,903,921,939,949,973,993

%N Nonprime and squarefree Löschian numbers (A003136).

%C 5187 is the first term that has 4 prime divisors.

%H Amiram Eldar, <a href="/A270667/b270667.txt">Table of n, a(n) for n = 1..10000</a>

%e 21 is a term because 21 = 3*7 = 4^2 + 4*1 + 1^2.

%t Select[Range[10^3], And[SquareFreeQ@ #, ! PrimeQ@ #, Resolve[Exists[{x, y}, Reduce[# == x^2 + x y + y^2, {x, y}, Integers]]]] &] (* _Michael De Vlieger_, Mar 21 2016, after _Jean-François Alcover_ at A003136 *)

%o (PARI) x='x+O('x^1000); p=eta(x)^3/eta(x^3); for(n=0, 999, if(polcoeff(p, n) != 0 && issquarefree(n) && !isprime(n), print1(n, ", ")));

%Y Cf. A003136, A005117, A034021.

%K nonn

%O 1,2

%A _Altug Alkan_, Mar 21 2016