A068314

[Don Reble]

Franklin, Seqfans:

> The main list is where some a(n) is not known, but a(m) for some m>n is
> known...

    Well, A068314 is easy. (%N: Smallest integer that can be expressed
    as the sum of consecutive odd numbers in exactly n ways.)
    A sum of consecutive odd numbers is a difference of two squares,
    and thus a factorization into odd*odd or even*even.
    For f(x) = the number of factors of x,
    - an odd number x has ceil(f(x)/2) representations;
    - a singly-even number has none;
    - 4*x has ceil(f(x)/2) representations.

    So a(n) is the smallest odd number with 2n-1 or 2n factors,
    or four times the smallest number with 2n-1 or 2n factors.


njas:

%I A068314
%S A068314 1,9,45,96,144,240,768,480,720,960,2304,1440,5184,3600,2880,3360,
%T A068314 36864,5040,3145728,6720,11520,61440,14400,10080,25920,245760,25200,
%U A068314 26880,9437184,20160,12884901888,30240,184320,3932160,103680,40320
%Y A068314 Cf. A001227, A005179, A034178, A038547, A038548.
%E A068314 More terms from Don Reble (djr(AT)nk.ca), Sep 08 2006

Copy http://www.graysage.com/djr/oeisB005179.txt ,
     http://www.graysage.com/djr/oeisB038547.txt ,
     http://www.graysage.com/djr/oeisB068314.txt , if you want.

-- 
Don Reble  djr at nk.ca


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