Two messgaes

[Antreas P. Hatzipolakis]

FWD MESSAGE ------------------------------------------------------------

Subject: Re: Describe These Numbers (solution)
From: Leroy Quet <qqquet at hotbot.com>
Date: 19 Oct 99 13:53:06 -0400 (EDT)
Newsgroup: sci.math

I, Leroy Quet wrote:

>Inspired by Clive Tooth's post, I give you my own number puzzle.
>Find the simplest definition for the following numbers.
>I've included all of them <=100.
>
>1,2,4,6,8,10,12,16,18,20,24,27,28,30,32,36,40,42,45,48,
>52,54,56,60,64,66,70,72,76,78,80,82,84,90,96,100
>
>I'll post my solution soon if no one else solves it sooner.

These numbers are the positive integers, n, where the number of
positive divisors of n! is divisible by n.
Thanks,
Leroy Quet

END ------------------------------------------------------------------------

and one from a friend:

<quote>
     A colleague of mine presented me with a sequence and challenged me to
find the recursion formula for it.
After trying several known techniques - I began to 'cheat' and looked
in my copy of Sloane's encyclopedia - to no avail.
Can you help?
1    1    4    14    46    146    454    (1394)    (4246)
                                         ^^^^^^^^^^^^^^^^
                                   My predictions based on my work.
</quote>


Antreas