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A079897
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a(1) = 1; a(n) = sigma(n) - sigma(n-1)* a(n-1) if n > 1.
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0
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1, 2, -2, 15, -99, 606, -7264, 58127, -871892, 11334614, -204023040, 2448276508, -68551742210, 959724390964, -23033385383112, 552801249194719, -17136838725036271, 308463097050652917, -12030060784975463743, 240601215699509274902, -10105251059379389545852
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..21.
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MATHEMATICA
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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]
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CROSSREFS
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Sequence in context: A216613 A215900 A184718 * A097540 A112327 A152541
Adjacent sequences: A079894 A079895 A079896 * A079898 A079899 A079900
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KEYWORD
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sign
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Feb 20 2003
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STATUS
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approved
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