

A348828


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


1



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
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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



