OFFSET
1,2
COMMENTS
This is to A008472 as A051448 is to A001414. It does seem that for any given k there should be a maximum n such that the sum of the prime factors of n = k^2, and a (perhaps different) maximum n such that the sum of distinct prime factors on n = k^2.
If k >= 3 and p = k^2 - 2 is prime (see A028870) then 2 * p is the term. - Marius A. Burtea, Jun 12 2019
LINKS
Marius A. Burtea, Table of n, a(n) for n = 1..14587 (terms up to 10^6)
EXAMPLE
a(7) = 66 because 66 = 2 * 3 * 11 has sum of distinct prime factors 2 + 3 + 11 = 16 = 4^2. 8748 = 2^2 * 3^7 is the largest number whose prime factors (with multiplicity) add to 25 = 5^2, but it is not in this sequence because the sum of distinct prime factors of 8748 is 2 + 3 = 5, which is not a square.
MATHEMATICA
Select[Range[600], IntegerQ[Sqrt[Total[Transpose[FactorInteger[#]] [[1]]]]]&] (* Harvey P. Dale, Mar 05 2014 *)
PROG
(PARI) isOK(n) = local(fac, i); fac = factor(n); issquare(sum(i=1, matsize(fac)[1], fac[i, 1])); \\ Michel Marcus, Mar 19 2013
(Magma) [n:n in [1..600]| IsPower(&+PrimeDivisors(n), 2)]; // Marius A. Burtea, Jun 12 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Aug 23 2009
EXTENSIONS
More terms (including missing terms 56, 183, and 196) from Jon E. Schoenfield, May 27 2010
STATUS
approved