cp's OEIS Frontend

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

%I A085018 #22 Oct 31 2016 10:21:30
%S A085018 1,4,13,24,33,37,52,61,69,73,88,97,109,121,132,141,157,177,181,184,
%T A085018 193,213,229,241,244,249,253,277,292,312,313,321,337,349,373,376,388,
%U A085018 393,397,409,421,429,433,457,472,481,501,517,529,537,541,564,568,573,577
%N A085018 Numbers n such that there is no divisor m of n with m<n and A083752(n) = (n/m)A083752(m).
%C A085018 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
%H A085018 N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)
%e A085018 A083752(2) = (2/1)*A083752(1), therefore 2 is not in the sequence.
%e A085018 But A083752(4) = 109 and 4*A083752(1) = 1572 and 2*A083752(2) = 1572.
%e A085018 Therefore the equation cannot be solved and 4 is in the sequence.
%t A085018 (* 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 *)
%o A085018 (Sage)
%o A085018 def is_A085018(n):
%o A085018     for d in divisors(n):
%o A085018         if d < n:
%o A085018             if d*A083752(n) == n*A083752(d):
%o A085018                 return false
%o A085018     return true
%o A085018 filter(is_A085018, (1..577)) # _Peter Luschny_, Jun 25 2014
%Y A085018 Cf. A083752, A085019, A244291, A243168.
%K A085018 nonn
%O A085018 1,2
%A A085018 _Zak Seidov_, Jun 18 2003
%E A085018 Edited and extended by _Stefan Steinerberger_, Jul 30 2007
%E A085018 More terms from _Peter Luschny_, Jun 25 2014