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 _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun