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

1,2

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.

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A099377, A099378.

Sequence in context: A079588 A100147 A117750 * A158462 A064495 A267904

Adjacent sequences: A348825 A348826 A348827 * A348829 A348830 A348831

Keyword

nonn

Author

Amiram Eldar, Nov 01 2021

Status

approved