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 -----
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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