A055041 Numbers of the form 3^(2i+1)*(3*j+1).

3, 12, 21, 27, 30, 39, 48, 57, 66, 75, 84, 93, 102, 108, 111, 120, 129, 138, 147, 156, 165, 174, 183, 189, 192, 201, 210, 219, 228, 237, 243, 246, 255, 264, 270, 273, 282, 291, 300, 309, 318, 327, 336, 345, 351, 354, 363, 372, 381, 390, 399

Offset

1,1

Comments

The numbers not of the form x^2+y^2+6z^2.

Numbers whose squarefree part is congruent to 3 modulo 9. Compare with A329575. - Peter Munn, May 17 2020

The asymptotic density of this sequence is 1/8. - Amiram Eldar, Mar 08 2021

Links

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

L. J. Mordell, A new Waring's problem with squares of linear forms, Quart. J. Math., 1 (1930), 276-288 (see p. 283).

Formula

a(n) = A055047(n) * 3. - Peter Munn, May 17 2020

Mathematica

f[p_, e_] := (p^Mod[e, 2]); sqfpart[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[400], Mod[sqfpart[#], 9] == 3 &] (* Amiram Eldar, Mar 08 2021 *)

Crossrefs

Intersection of A145204 and A189716.

Complement of A055040 with respect to A145204\{0}.

Complement of A055048 with respect to A189716.

Cf. A007913, A055047, A329575.

Sequence in context: A080767 A043465 A074276 * A061819 A017197 A051369

Adjacent sequences: A055038 A055039 A055040 * A055042 A055043 A055044

Keyword

nonn

Author

N. J. A. Sloane, Jun 01 2000

Status

approved