A085018 Numbers n such that there is no divisor m of n with m<n and A083752(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

1,2

Comments

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

Links

Table of n, a(n) for n=1..55.

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

Example

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.

Mathematica

(* 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 *)

Prog

(Sage)
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

Crossrefs

Cf. A083752, A085019, A244291, A243168.

Sequence in context: A031320 A112263 A244291 * A255840 A001741 A272702

Adjacent sequences: A085015 A085016 A085017 * A085019 A085020 A085021

Keyword

nonn

Author

Zak Seidov, Jun 18 2003

Extensions

Edited and extended by Stefan Steinerberger, Jul 30 2007

More terms from Peter Luschny, Jun 25 2014

Status

approved