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 A079897 a(1) = 1; a(n) = sigma(n) - sigma(n-1)* a(n-1) if n > 1. 0
 1, 2, -2, 15, -99, 606, -7264, 58127, -871892, 11334614, -204023040, 2448276508, -68551742210, 959724390964, -23033385383112, 552801249194719, -17136838725036271, 308463097050652917, -12030060784975463743, 240601215699509274902, -10105251059379389545852 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified December 2 05:01 EST 2021. Contains 349437 sequences. (Running on oeis4.)