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.)

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

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: A161278 A160982 A334541 * 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