%I A117825
%S A117825 1,0,1,1,1,1,1,1,1,7,1,1,1,1,1,1,11,1,1,1,1,1,1,11,13,1,11,1,17,1,1,
%T A117825 13,13,1,1,17,1,17,1,1,17,17,17,1,1,19,37,37,1,17,23,1,29,1,1,19,1,19,
%U A117825 23,1,19,31,1,19,1,1,1,1,23,1,29,23,23,1,23,71,37,1,1,31,1,23,53,1,31
%N A117825 Distance from n-th highly composite number (cf. A002182) to nearest prime.
%C A117825 a) Conjecture: entries > 1 will always be prime. The entry will be larger 
               than the largest prime factor of the highly composite number.
%C A117825 b) Will 1 always be the most common entry?
%C A117825 c) While a prime may always located close to each highly composite number, 
               is the converse false?
%C A117825 d) Is there always a prime between successive highly composite numbers?
%H A117825 Charles Greathouse IV, <a href="b117825.txt">Table of n, a(n) for n = 
               1..19999</a>
%H A117825 Graeme McRae, <a href="http://2000clicks.com/MathHelp/NumberFactorsHighlyComposite.htm">
               Highly Composite Numbers</a>
%H A117825 Wikipedia, <a href="http://en.wikipedia.org/wiki/Highly_composite">Highly 
               Composite Numbers</a>.
%H A117825 Wikipedia, <a href="http://en.wikipedia.org/wiki/Divisor_function">Divisor 
               Function (sigma)</a>.
%H A117825 Wikimedia Commons,<a href="http://commons.wikimedia.org/wiki/File:OEIS_A117825.jpg">
               Alternate plot</a>
%e A117825 a(5) = abs(12-11)=1.
%Y A117825 Sequence in context: A074465 A081229 A109010 this_sequence A010143 A101027 
               A129408
%Y A117825 Adjacent sequences: A117822 A117823 A117824 this_sequence A117826 A117827 
               A117828
%K A117825 nonn
%O A117825 1,10
%A A117825 Bill McEachen, May 01 2006
%E A117825 More terms from Don Reble (djr(AT)nk.ca), May 02 2006