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
Keywords
Examples
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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..500
Programs
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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