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A175150 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.) 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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)).

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

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Last modified November 21 22:32 EST 2017. Contains 295054 sequences.