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
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
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Aug 26 2009
EXTENSIONS
More terms from Jon E. Schoenfield, May 27 2010
STATUS
approved