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A002481
Numbers of form x^2 + 6y^2.
(Formerly M3269 N1320)
18
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
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
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 (terms <= 10000).
Leonhard Euler, E388 Vollständige Anleitung zur Algebra, Zweiter Theil, reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 1, p. 425.
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
Sequence in context: A189715 A101993 A370267 * A370268 A183870 A186497
KEYWORD
nonn
STATUS
approved