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A002481 Numbers of form x^2 + 6y^2.

%I A002481 M3269 N1320 #32 Feb 05 2020 10:37:10
%S A002481 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,
%T A002481 70,73,79,81,87,88,90,96,97,100,103,105,106,112,118,121,124,127,132,
%U A002481 135,144,145,150,151,154,159,160,166,168,169,175,177,186,193,196,198,199,202,214
%N A002481 Numbers of form x^2 + 6y^2.
%C A002481 Norms of numbers in Z[sqrt(-6)]. - _Alonso del Arte_, Sep 23 2014
%C A002481 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
%D A002481 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002481 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002481 Zak Seidov, <a href="/A002481/b002481.txt">Table of n, a(n) for n = 1..2064</a> (terms <= 10000).
%H A002481 Leonhard Euler, <a href="http://eulerarchive.maa.org/pages/E388.html">E388 Vollständige Anleitung zur Algebra, Zweiter Theil</a>, reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 1, p. 425.
%p A002481 N:= 10^4: # to get all terms <= N
%p A002481 {seq(seq(a^2 + 6*b^2, a = 0 .. floor(sqrt(N-6*b^2))), b = 0 .. floor(sqrt(N/6)))};
%p A002481 # for Maple 11, or earlier, uncomment the next line
%p A002481 # sort(convert(%,list));  # _Robert Israel_, Sep 24 2014
%t A002481 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 *)
%Y A002481 Cf. A020669, A033199.
%K A002481 nonn
%O A002481 1,3
%A A002481 _N. J. A. Sloane_