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A002481 Numbers of form x^2 + 6y^2.
(Formerly M3269 N1320)
14
0, 1, 4, 6, 7, 9, 10, 15, 16, 22, 24, 25, 28, 31, 33, 36, 40, 42, 49, 54, 55, 58, 60, 63, 64, 70, 73, 79, 81, 87, 88, 90, 96, 97, 100, 103, 105, 106, 112, 118, 121, 124, 127, 132, 135, 144, 145, 150, 151, 154, 159, 160, 166, 168, 169, 175, 177, 186, 193, 196, 198, 199, 202, 214 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Norms of numbers in Z[sqrt(-6)]. - Alonso del Arte, Sep 23 2014

It seems that a positive integer n is in this sequence if and only if the p-adic order ord_p(n) of n is even for any prime p with floor(p/12) odd, and the number of prime divisors p == 5 or 11 (mod 24) with ord_p(n) odd has the same parity with ord_2(n) + ord_3(n). - Zhi-Wei Sun, Mar 24 2018

REFERENCES

Leonhard Euler, (E388) Vollstaendige Anleitung zur Algebra, Zweiter Theil, reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 1, p. 425.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Zak Seidov, Table of n, a(n) for n = 1..2064 (with a(n) <= 10000)

MAPLE

N:= 10^4: # to get all terms <= N

{seq(seq(a^2 + 6*b^2, a = 0 .. floor(sqrt(N-6*b^2))), b = 0 .. floor(sqrt(N/6)))};

# for Maple 11, or earlier, uncomment the next line

# sort(convert(%, list));  # Robert Israel, Sep 24 2014

MATHEMATICA

lim = 10^4; k = 6; Union@Flatten@Table[x^2 + k * y^2, {y, 0, Sqrt[lim/k]}, {x, 0, Sqrt[lim - k * y^2]}] (* Zak Seidov, Mar 30 2011 *)

CROSSREFS

Cf. A020669, A033199.

Sequence in context: A069909 A189715 A101993 * A183870 A186497 A193627

Adjacent sequences:  A002478 A002479 A002480 * A002482 A002483 A002484

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 16 02:39 EST 2019. Contains 320140 sequences. (Running on oeis4.)