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%I #17 Mar 11 2014 01:32:50
%S 0,1,1,2,1,2,1,2,1,2,1,2,1,2,2,3,2,3,2,3,2,2,1,2,1,2,2,3,2,3,2,3,2,2,
%T 2,3,2,3,3,4,3,4,3,4,4,3,2,3,2,3,2,3,2,3,2,3,2,2,1,2,1,2,3,4,3,4,3,4,
%U 3,4,3,4,3,4,5,5,4,5,4,5,4,3,2,3,2,2,2,3
%N a(1)=0. If d(n)>d(n-1), then a(n)=a(n-1)+1. If d(n)<d(n-1), then a(n)=a(n-1)-1. If d(n)=d(n-1), then a(n)=a(n-1). (d(n) is the number of divisors of n.)
%C For n >=2, a(n) = (the number of k <= n where d(k) > d(k-1)) - (the number of k <= n where d(k) < d(k-1)).
%C The record values of {a(n)} occur at n= 1, 2, 4, 16, 40, 75, 165, 208,...
%C This sequence goes negative at n = 647. In the plot of the first 10^6 terms, the graph is mostly negative after about 250000. - _T. D. Noe_, Apr 27 2012
%H T. D. Noe, <a href="/A175150/b175150.txt">Table of n, a(n) for n = 1..10000</a>
%H T. D. Noe, <a href="/A175150/a175150.gif">Plot of 10^6 terms</a>
%t Join[{0}, Accumulate[Sign[Differences[DivisorSigma[0, Range[100]]]]]] (* _T. D. Noe_, Apr 27 2012 *)
%Y Cf. A000005, A182394 (first differences).
%K sign
%O 1,4
%A _Leroy Quet_, Feb 24 2010
%E Extended by _Ray Chandler_, Mar 03 2010
%E Comment typo corrected by _Leroy Quet_, Mar 07 2010
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