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A085018
Numbers n such that there is no divisor m of n with m<n and A083752(n) = (n/m)A083752(m).
4
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
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
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