A164788 Numbers such that the sum of the distinct prime factors is a cube.
1, 15, 45, 75, 135, 183, 225, 285, 295, 354, 357, 375, 405, 429, 510, 549, 583, 675, 708, 799, 855, 910, 943, 1020, 1055, 1062, 1071, 1125, 1215, 1266, 1287, 1416, 1425, 1454, 1475, 1527, 1530, 1634, 1647, 1820, 1875, 2025, 2040, 2124, 2499, 2532, 2550, 2565
Offset: 1
Examples
a(2) = 15 because 15 = 3 * 5, the sum of distinct prime factors being 3+5 = 8 = 2^3. a(5) = 183 = 3 * 61 because 3 + 61 = 64 = 4^3. a(7) = 285 because 285 = 3 * 5 * 19 and 3 + 5 + 19 = 27 = 3^3.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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Magma
[n:n in [1..2600]| IsPower(&+PrimeDivisors(n), 3)]; // Marius A. Burtea, Jun 30 2019
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Mathematica
Select[Range[3000],IntegerQ[Surd[Total[Transpose[FactorInteger[#]][[1]]],3]]&] (* Harvey P. Dale, Jun 21 2013 *)
Extensions
More terms from Jon E. Schoenfield, May 27 2010
Comments