Numbers of the third kind

[Jaap Spies]

> Superseeker returned:
> Report on [ 6,9,10,12,14,15,18,20,21,22,24,25,26,27,28,30,33,34,35,36,38,39]:
> Many tests are carried out, but only potentially useful information
> (if any) is reported here.
> 
> Even though there are a large number of sequences in the table, at least
> one of yours is not there!


Let's see what is so special about this numbers.
1. there are no (odd) primes;
2. there are no powers of 2.

The numbers in the sequence can be written as a sum of at least three
positive integers. See:
    http://www.jaapspies.nl/mathfiles/problem2005-2C.pdf
Solution of Problem C from the UWC of Nieuw Archief voor Wiskunde:
http://www.math.leidenuniv.nl/%7Enaw/serie5/index.php?deel=6&nummer=2&taal=1

So we have only three kinds of natural numbers: the odd primes, the
powers of 2 and numbers that can be represented as sum of at least
three integers.

Comments?

I will submit this and two related sequences shortly,

Jaap Spies