A348828 - OEIS

%I #12 Nov 02 2021 06:30:22

%S 1,30,138,210,2280,4676,5970,6972,8372,10290,12012,12306,20370,22386,

%T 105420,116844,118524,153480,189420,195860,204204,218430,289560,

%U 293880,362180,369740,408510,414990,494760,525420,629640,933660,952770,1529010,1564332,1647810

%N Numbers that are equal to the product of the numerator and denominator of the harmonic mean of their divisors.

%C Numbers k such that A099377(k) * A099378(k) = k.

%C Is 1 the only odd term? There are no other odd terms below 3*10^9.

%H Amiram Eldar, <a href="/A348828/b348828.txt">Table of n, a(n) for n = 1..1000</a>

%e 30 is a term since the harmonic mean of its divisors is 10/3 and 10*3 = 30.

%e 138 is a term since the harmonic mean of its divisors is 23/6 and 23*6 = 138.

%t q[n_] := Numerator[(hm = DivisorSigma[0, n]/DivisorSigma[-1, n])] * Denominator[hm] == n; Select[Range[10^6], q]

%o (PARI) isok(k) = my(d=divisors(k), h=#d/sum(i=1, #d, 1/d[i])); k == numerator(h)*denominator(h); \\ _Michel Marcus_, Nov 01 2021

%Y Cf. A099377, A099378.

%K nonn

%O 1,2

%A _Amiram Eldar_, Nov 01 2021