A270667 Nonprime and squarefree Löschian numbers (A003136).

1, 21, 39, 57, 91, 93, 111, 129, 133, 183, 201, 217, 219, 237, 247, 259, 273, 291, 301, 309, 327, 381, 399, 403, 417, 427, 453, 469, 471, 481, 489, 511, 543, 553, 559, 579, 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

Offset: 1

Author

Altug Alkan, Mar 21 2016

Keywords

• nonn

Comments

5187 is the first term that has 4 prime divisors.

Examples

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

Links

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

Crossrefs

Cf. A003136, A005117, A034021.

Programs

Mathematica

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 *)

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, ", ")));