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%I #13 May 09 2019 15:01:07
%S 1,9,45,96,144,240,768,480,720,960,2304,1440,5184,3600,2880,3360,
%T 36864,5040,3145728,6720,11520,61440,14400,10080,25920,245760,25200,
%U 26880,9437184,20160,12884901888,30240,184320,3932160,103680,40320
%N Smallest integer that can be expressed as the sum of consecutive odd numbers in exactly n ways.
%C The sequence continues: ?,30240,184320,3932160,103680,40320,?,129600,737280,60480,176400,80640,?,430080,100800 where ? is a value > 20000000. A value always exists since 3*(2^(i+1)) is an upper bound for the i-th term (i odd) and 5*3*(2^((i+2)/2)) is an upper bound for i even. Based on these limits, the bounds on the 31st, 37th and 43rd terms are 12884901888, 824633720832 and 52776558133248 respectively. - Larry Reeves (larryr(AT)acm.org), Dec 18 2002
%C Also the smallest integer that can be expressed as a difference of squares in exactly n ways. - _J. M. Bergot_, May 09 2019
%H Don Reble, <a href="/A068314/b068314.txt">Table of n, a(n) for n = 1..2000</a>
%e 45 = 45 = 13+15+17 = 5+7+9+11+13, 45 is the smallest number expressible in 3 ways, so a(3)=45.
%Y Cf. A038548, A034178, A001227.
%K nonn
%O 1,2
%A _Naohiro Nomoto_, Feb 26 2002
%E More terms from Larry Reeves (larryr(AT)acm.org), Dec 18 2002
%E Further terms from _Don Reble_, Sep 08 2006
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