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%I #21 Nov 10 2016 08:11:23
%S 5,2,3,13,17,5,21,6,7,29,2,33,37,10,41,11,5,3,13,53,14,57,15,61,65,17,
%T 69,2,73,19,77,5,21,85,22,89,23,93,6,97,101,26,105,3,109,7,113,29,13,
%U 30,31,5,2,129,33,133,34,137,35,141,145,37,149,38,17,39,157,10
%N Squarefree parts of A079896(n), n>= 0.
%C a(n) is the squarefree part of the discriminant D(n) = A079896(n) of indefinite binary quadratic forms. Certain quadratic irrationals, called omega_p(D(n)), related to the principal indefinite form of discriminant D(n) are integers in the quadratic number field Q(sqrt(a(n))). See A226166 for the definition of these irrationals omega_p(D(n)) using the D. A. Buell reference, p. 31 and p. 26.
%C For discriminants D == 1 (mod 4) these squarefree parts are given in A226165. For D == 0 (mod 4) the squarefree parts are given in A002734 corresponding to A000037 = D/4.
%D D. A. Buell, Binary Quadratic Forms, Springer, 1989.
%H Gheorghe Coserea, <a href="/A226693/b226693.txt">Table of n, a(n) for n = 0..20000</a>
%F a(n) = squarefree part of D(n) = A079896(n), n >= 0, the numbers 0 and 1 (mod 4), not a square.
%t SquareFreePart[n_] := Times @@ Power @@@ ({#[[1]], Mod[#[[2]], 2]} & /@ FactorInteger[n]); SquareFreePart /@ Select[ Range[160], ! IntegerQ[Sqrt[#]] && Mod[#, 4] < 2 &] (* _Jean-François Alcover_, Jun 25 2013 *)
%o (PARI)
%o A079896_list(N) = {
%o my(n = 1, v = vector(N), top = 0);
%o while (top < N, if (n%4 < 2 && !issquare(n), v[top++] = n); n++;);
%o return(v);
%o };
%o apply(core, A079896_list(68)) \\ _Gheorghe Coserea_, Nov 10 2016
%Y Cf. A079896, A226165, A002734.
%K nonn,easy
%O 0,1
%A _Wolfdieter Lang_, Jun 15 2013
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