A270672 Löschian numbers (A003136) that are multiples of 3.

0, 3, 9, 12, 21, 27, 36, 39, 48, 57, 63, 75, 81, 84, 93, 108, 111, 117, 129, 144, 147, 156, 171, 183, 189, 192, 201, 219, 225, 228, 237, 243, 252, 273, 279, 291, 300, 309, 324, 327, 333, 336, 351, 363, 372, 381, 387, 399, 417, 432, 441, 444, 453, 468, 471, 489, 507, 513, 516, 525, 543, 549

Offset

1,2

Comments

Numbers of the form 3*(x^2 + xy + y^2).

Intersection of A008585 and A003136.

Links

Charles R Greathouse IV, 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[0, 600], Resolve[Exists[{x, y}, Reduce[# == 3 (x^2 + x y + y^2), {x, y}, Integers]]] &] (* Michael De Vlieger, Mar 21 2016 *)

Prog

(PARI) x='x+O('x^1000); p=eta(x)^3/eta(x^3); for(n=0, 999, if(polcoeff(p, n) != 0 && n % 3 == 0, print1(n, ", ")));
(PARI) list(lim)=my(v=List(), y, t); for(x=0, sqrtint(lim\3), my(y=x, t); while((t=x^2+x*y+y^2)<=lim, listput(v, t); y+=3)); Set(v) \\ Charles R Greathouse IV, Jul 05 2017

Crossrefs

Cf. Loeschian numbers: A003136 (all), A270248 (2*k), A266836 (2*k+1), A202822 (3*k+1), A260682 (6*k+1).

Sequence in context: A212059 A226152 A155504 * A211217 A307201 A022379

Adjacent sequences: A270669 A270670 A270671 * A270673 A270674 A270675

Keyword

nonn

Author

Altug Alkan, Mar 21 2016

Status

approved