A074266 Numbers k such that the harmonic mean of the divisors of k is the square of a rational number.

1, 216, 468, 810, 1550, 1638, 3744, 10880, 11340, 13965, 21700, 23716, 40176, 45847, 50274, 56896, 80262, 90720, 97969, 126360, 128744, 137940, 139159, 161728, 173600, 189728, 224450, 319579, 434511, 482790, 515450, 526500, 555660

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..500

Example

The harmonic mean of the divisors of 468 is 324/49 = (18/7)^2, the square of a rational number, so 468 is a term of the sequence.

Mathematica

H[l_] := Module[{m, s}, m = Length[l]; s = 0; For[i = 1, i <= m, i++, s = s + (1/l[[i]])]; s = s/m; s = 1/s; s] r = {}; Do[d = Divisors[n]; h = H[d]; num = Numerator[h]; den = Denominator[h]; If[IntegerQ[num^(1/2)] && IntegerQ[den^(1/2)], r = Append[r, n]], {n, 1, 10^6}]; r

Crossrefs

Cf. A001599, A099377, A099378.

Sequence in context: A372695 A043371 A304369 * A208089 A333316 A275154

Adjacent sequences: A074263 A074264 A074265 * A074267 A074268 A074269

Keyword

nonn

Author

Joseph L. Pe, Sep 20 2002

Status

approved