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%I #16 Feb 01 2021 19:28:55
%S 1,4,9,12,16,18,25,36,45,48,49,64,72,81,100,108,112,121,144,150,162,
%T 169,180,192,196,225,240,256,288,289,294,300,324,361,396,400,405,432,
%U 441,448,450,484,490,525,529,576,588,600,625,637,648,676,720,729,768,784,841,882,900,960,961
%N Numbers k with a divisor pair (d,k/d) whose harmonic mean is an integer.
%C 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.
%e 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).
%e 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).
%t seqQ[n_] := Module[{d = Select[Divisors[n], #^2 <= n &]}, AnyTrue[d, IntegerQ @ HarmonicMean[{#, n/#}] &]]; Select[Range[1000], seqQ] (* _Amiram Eldar_, Aug 18 2020 *)
%o (PARI) isok(k) = {fordiv(k, d, if (denominator(2*k*d/(d^2+k)) == 1, return (1)););} \\ _Michel Marcus_, Aug 16 2020
%Y Cf. A000290.
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, Aug 16 2020
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