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

1,2

Comments

This is the 3rd row of the infinite array A(k,n) = n-th positive integer such that the sum of the distinct prime factors is of the form j^k for integers j, k. The 2nd row is A164722.

If k >= 1 and p = (2*k)^3 - 5 is prime (see A200957) then 5*p is a term. - Marius A. Burtea, Jun 30 2019

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

{n such that A008472(n) = k^3 for k an integer}. {n such that A008472(n) is in A000578}.

Example

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.

Mathematica

Select[Range[3000], IntegerQ[Surd[Total[Transpose[FactorInteger[#]][[1]]], 3]]&] (* Harvey P. Dale, Jun 21 2013 *)

Prog

(Magma) [n:n in [1..2600]| IsPower(&+PrimeDivisors(n), 3)]; // Marius A. Burtea, Jun 30 2019

Crossrefs

Cf. A000578, A008472, A164722.

Sequence in context: A345654 A298462 A066763 * A033849 A194715 A060536

Adjacent sequences: A164785 A164786 A164787 * A164789 A164790 A164791

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 26 2009

Extensions

More terms from Jon E. Schoenfield, May 27 2010

Status

approved