A348828 Numbers that are equal to the product of the numerator and denominator of the harmonic mean of their divisors.

1, 30, 138, 210, 2280, 4676, 5970, 6972, 8372, 10290, 12012, 12306, 20370, 22386, 105420, 116844, 118524, 153480, 189420, 195860, 204204, 218430, 289560, 293880, 362180, 369740, 408510, 414990, 494760, 525420, 629640, 933660, 952770, 1529010, 1564332, 1647810

Offset: 1

Author

Amiram Eldar, Nov 01 2021

Keywords

• nonn

Comments

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

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

Examples

			30 is a term since the harmonic mean of its divisors is 10/3 and 10*3 = 30.
138 is a term since the harmonic mean of its divisors is 23/6 and 23*6 = 138.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A099377, A099378.

Programs

Mathematica

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

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