A033677 is the smallest divisor of n >= sqrt(n).  The Maple program
given for this looks quite inefficient.  It appears to obtain the divisors
of n, then compare them all to the sqrt(n).  A033677(n) will be the
central element or larger of two central elements of the sorted list
of divisors of n.  You do not need to compute sqrt(n) to obtain this
value.
 
----- Original Message -----
From: Michael Kleber
To: math-fun
Sent: Saturday, July 05, 2003 10:46 PM
Subject: Re: [math-fun] Annoyed

> A027424 annoys me.

Yes, I agree.

For the record, the sort-of complementary problem is
A033677: Smallest divisor of n >= sqrt(n).
Then A033677(n) is the smallest k such that n appears
in the k-by-k multiplication table, and A027424(k)
is the number of n with A033677(n) <= k.  These seq's
should probably be cross-linked to each other.

I agree with Rich that maybe the first differences seem
easier to attack, but this might be deceptive... this is
asking how many of {n,2n,3n,...,n^2} are not ij for
i,j<n, and doing this based on the factorization of n
means recognizing things like "No, 34*16 isn't new
for n=34, because it already appeared as 32*17."
Maybe for each n you can look at its prime factorization
and calculate one list of likely factor swaps to look out
for?  Ugh.

--Michael Kleber
   kleber@brandeis.edu


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