A079897 a(1) = 1; a(n) = sigma(n) - sigma(n-1)* a(n-1) if n > 1.

1, 2, -2, 15, -99, 606, -7264, 58127, -871892, 11334614, -204023040, 2448276508, -68551742210, 959724390964, -23033385383112, 552801249194719, -17136838725036271, 308463097050652917, -12030060784975463743, 240601215699509274902, -10105251059379389545852

Offset

1,2

Comments

1. Let s(n) be a sequence such that lim s(n)/s(n+1) = K different from -1. The "oscillator sequence" (or simply "oscillator") of s(n) is the sequence s'(n) defined by the rules: s'(1) = 1; s'(n) = 1 - (s(n-1)/s(n)) s'(n-1). 2. It is an open problem whether the oscillator (prime)' converges to 1/2 or diverges. 3. s'(n) = 1 - (s(n-1)/s(n)) s'(n-1) = [s(n) - s(n-1) s'(n-1)]/s(n). The numerator is the expression s(n) - s(n-1) s'(n-1), which motivates the definition of the above sequence a(n). a(n) is called the "integral oscillator" of sigma(n). In general the integral oscillator of s(n) can be defined similarly.

Links

Table of n, a(n) for n=1..21.

Mathematica

t = {1}; gt = 1; For[i = 2, i <= 30, i++, gt = DivisorSigma[1, i] - DivisorSigma[1, i - 1] gt; t = Append[t, gt]]; t ListPlot[t, PlotJoined -> True]

Crossrefs

Sequence in context: A215900 A264838 A184718 * A097540 A345225 A112327

Adjacent sequences: A079894 A079895 A079896 * A079898 A079899 A079900

Keyword

sign

Author

Joseph L. Pe, Feb 20 2003

Status

approved