A244291 -id:A244291 - 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

A243168 Nonnegative integers of the form x^2 + 6xy - 3y^2.

Original entry on oeis.org

0, 1, 4, 9, 13, 16, 24, 25, 33, 36, 37, 49, 52, 61, 64, 69, 73, 81, 88, 96, 97, 100, 109, 117, 121, 132, 141, 144, 148, 157, 169, 177, 181, 184, 193, 196, 208, 213, 216, 225, 229, 241, 244, 249, 253, 256, 276, 277, 289, 292, 297, 312, 313, 321, 324, 325, 333, 337, 349, 352, 361, 373, 376, 384, 388, 393, 397, 400, 409, 421, 429, 433, 436, 441, 457, 468, 472

Offset: 1

N. J. A. Sloane, Jun 01 2014

nonn

Discriminant 48.

Also nonnegative integers of the form 4x^2 - 3y^2. - Jon E. Schoenfield, Jun 03 2022

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

Primes in this sequence = A068228. Cf. A085018, A244291.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Sage

Extensions