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 A270672 Löschian numbers (A003136) that are multiples of 3. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified March 3 07:26 EST 2024. Contains 370499 sequences. (Running on oeis4.)