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

1,2

Comments

5187 is the first term that has 4 prime divisors.

Links

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

Example

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

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 *)

Prog

(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, ", ")));

Crossrefs

Cf. A003136, A005117, A034021.

Sequence in context: A338552 A339002 A339004 * A020220 A251122 A084856

Adjacent sequences: A270664 A270665 A270666 * A270668 A270669 A270670

Keyword

nonn

Author

Altug Alkan, Mar 21 2016

Status

approved