

A175150


a(1)=0. If d(n)>d(n1), then a(n)=a(n1)+1. If d(n)<d(n1), then a(n)=a(n1)1. If d(n)=d(n1), then a(n)=a(n1). (d(n) is the number of divisors of n.)


2



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, 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, 3, 4, 3, 4, 3, 4, 5, 5, 4, 5, 4, 5, 4, 3, 2, 3, 2, 2, 2, 3
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OFFSET

1,4


COMMENTS

For n >=2, a(n) = (the number of k <= n where d(k) > d(k1))  (the number of k <= n where d(k) < d(k1)).
The record values of {a(n)} occur at n= 1, 2, 4, 16, 40, 75, 165, 208,...
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


LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000
T. D. Noe, Plot of 10^6 terms


MATHEMATICA

Join[{0}, Accumulate[Sign[Differences[DivisorSigma[0, Range[100]]]]]] (* T. D. Noe, Apr 27 2012 *)


CROSSREFS

Cf. A000005, A182394 (first differences).
Sequence in context: A161303 A161278 A160982 * A161236 A161060 A161264
Adjacent sequences: A175147 A175148 A175149 * A175151 A175152 A175153


KEYWORD

sign


AUTHOR

Leroy Quet, Feb 24 2010


EXTENSIONS

Extended by Ray Chandler, Mar 03 2010
Comment typo corrected by Leroy Quet, Mar 07 2010


STATUS

approved



