[seqfan] Re: A060798 Difference between upper and lower central divisors of n is 1

[franktaw at netscape.net]

This is all screwed up.

A060775 is titled "Lower central (median) divisor of n." With that 
title, it is an incorrect version of A033676, "Largest divisor of n <= 
sqrt(n)." It could be retitled "Largest divisor of n < sqrt(n).", which 
would match the current values. A060798 then needs to be retitled 
something like "Difference between smallest divisor of n >= sqrt(n) and 
next smaller divisor is 1."

The 'formula' in A060798 "Solutions to A033677(n)-A060775(n)=1, where 
n=k*(k+1) and at least one of k and k+1 is composite." should become a 
comment, with the tail portion starting with ", where" deleted - n 
isn't k*(k+1) for n = 1 or 4, and for n = 6, neither k nor k+1 is 
composite. Additional comments are needed: "1 is arbitrarily included, 
even though it has no divisor < sqrt(n).", and "Same as A002378 with 
the additional elements 1 and 4."

Now Georgi's formula could be added to A002378; there is no need to say 
"except for the initial terms". The formula is a simple consequence of 
the g.f. for A002378, but it is probably worth adding explicitly.

Franklin T. Adams-Watters

-----Original Message-----
From: Georgi Guninski <guninski at guninski.com>

A060798 Difference between upper and lower central divisors of n is 1

except for the initial terms seems to satisfy:

a(n+1)=(3*a(n)-3*a(n-1)+a(n-2))