A243168 -id:A243168 - cp's OEIS frontend

A085018 Numbers n such that there is no divisor m of n with mA083752(n) = (n/m)A083752(m).

1, 4, 13, 24, 33, 37, 52, 61, 69, 73, 88, 97, 109, 121, 132, 141, 157, 177, 181, 184, 193, 213, 229, 241, 244, 249, 253, 277, 292, 312, 313, 321, 337, 349, 373, 376, 388, 393, 397, 409, 421, 429, 433, 457, 472, 481, 501, 517, 529, 537, 541, 564, 568, 573, 577

Offset: 1

Zak Seidov, Jun 18 2003

nonn

Seems to be a subsequence of the positive numbers primitively represented by the binary quadratic form (1, 6, -3) with discriminant 48 (see A244291, A243168). - Peter Luschny, Jun 25 2014

			A083752(2) = (2/1)*A083752(1), therefore 2 is not in the sequence.
But A083752(4) = 109 and 4*A083752(1) = 1572 and 2*A083752(2) = 1572.
Therefore the equation cannot be solved and 4 is in the sequence.

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Cf. A083752, A085019, A244291, A243168.

(* b = A083752 *) b[n_] := b[n] = For[k = n+1, True, k++, If[IntegerQ[Sqrt[(4k+3n)(4n+3k)]], Return[k]]]; Reap[For[n = 1, n < 600, n++, mm = Most @ Divisors[n]; If[NoneTrue[mm, b[n] == (n/#) b[#] &], Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Oct 31 2016 *)

def is_A085018(n):
    for d in divisors(n):
        if d < n:
            if d*A083752(n) == n*A083752(d):
                return false
    return true
filter(is_A085018, (1..577)) # Peter Luschny, Jun 25 2014

Edited and extended by Stefan Steinerberger, Jul 30 2007

More terms from Peter Luschny, Jun 25 2014

A244291 Positive numbers primitively represented by the binary quadratic form (1, 6, -3).

Original entry on oeis.org

1, 4, 13, 24, 33, 37, 52, 61, 69, 73, 88, 97, 109, 121, 132, 141, 148, 157, 169, 177, 181, 184, 193, 213, 229, 241, 244, 249, 253, 276, 277, 292, 312, 313, 321, 337, 349, 373, 376, 388, 393, 397, 409, 421, 429, 433, 436, 457, 472, 481, 484, 501, 517, 529, 537

Offset: 1

Peter Luschny, Jun 25 2014

nonn

Discriminant = 48.

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Cf. A085018, A244169. A subsequence of A243168.

Reap[For[n = 1, n < 1000, n++, r = Reduce[x^2 + 6 x y - 3 y^2 == n, {x, y}, Integers]; If[r =!= False, If[AnyTrue[{x, y} /. {ToRules[r /. C[1] -> 0]}, CoprimeQ @@ # &], Sow[n]]]]][[2, 1]] (* Jean-François Alcover, Oct 31 2016 *)

cp's OEIS Frontend

A085018 Numbers n such that there is no divisor m of n with mA083752(n) = (n/m)A083752(m).

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