OFFSET
1,2
COMMENTS
All positive squares are in the sequence since they have a divisor pair such that (d,k/d) = (d,d). The harmonic mean is then an integer since we have 2*d*d/(d+d) = 2*d*d/(2*d) = d.
EXAMPLE
18 is in the sequence since it has the divisor pair (3,6) with harmonic mean 2*3*6/(3+6) = 36/9 = 4 (an integer).
25 is in the sequence since it has the divisor pair (5,5) with harmonic mean 2*5*5/(5+5) = 50/10 = 5 (an integer).
MATHEMATICA
seqQ[n_] := Module[{d = Select[Divisors[n], #^2 <= n &]}, AnyTrue[d, IntegerQ @ HarmonicMean[{#, n/#}] &]]; Select[Range[1000], seqQ] (* Amiram Eldar, Aug 18 2020 *)
PROG
(PARI) isok(k) = {fordiv(k, d, if (denominator(2*k*d/(d^2+k)) == 1, return (1)); ); } \\ Michel Marcus, Aug 16 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 16 2020
STATUS
approved