

A068314


Smallest integer that can be expressed as the sum of consecutive odd numbers in exactly n ways.


16



1, 9, 45, 96, 144, 240, 768, 480, 720, 960, 2304, 1440, 5184, 3600, 2880, 3360, 36864, 5040, 3145728, 6720, 11520, 61440, 14400, 10080, 25920, 245760, 25200, 26880, 9437184, 20160, 12884901888, 30240, 184320, 3932160, 103680, 40320
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OFFSET

1,2


COMMENTS

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 ith 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
Also the smallest integer that can be expressed as a difference of squares in exactly n ways.  J. M. Bergot, May 09 2019


LINKS



EXAMPLE

45 = 45 = 13+15+17 = 5+7+9+11+13, 45 is the smallest number expressible in 3 ways, so a(3)=45.


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Dec 18 2002


STATUS

approved



