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1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1
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OFFSET
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1
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COMMENTS
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Also numerators of an infinite series which is equal to pi, if the denominators are the natural numbers A000027, for example: pi = 1/1 + 1/2 + 1/3 + 1/4 - 1/5 + 1/6 + 1/7 + 1/8 + 1/9 - 1/10 + 1/11 + 1/12 - 1/13 + 1/14 ... = 3.14159263... This remarkable result is due to Leonhard Euler. For another version see A209662.
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REFERENCES
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L. Euler, Introductio in analysin infinitorum, 1748.
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LINKS
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Ray Chandler, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = A209662(n)/n.
Completely multiplicative with a(p) = -1 for p mod 4 = 1, a(p) = 1 otherwise. - Andrew Howroyd, Aug 04 2018
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EXAMPLE
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For n = 10 we have that the 10th row of triangle A207338 is [2, -5] therefore a(10) = 2*(-5)/10 = -1.
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PROG
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(PARI) a(n)={my(f=factor(n)); prod(i=1, #f~, my([p, e]=f[i, ]); if(p%4==1, -1, 1)^e)} \\ Andrew Howroyd, Aug 04 2018
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CROSSREFS
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Row products of triangle A207338 divided by n. Absolute values give A000012.
Cf. A000027, A000796, A002144, A002145, A083025, A207338, A209662, A209921, A209922.
Sequence in context: A306638 A076479 A155040 * A033999 A000012 A216430
Adjacent sequences: A209658 A209659 A209660 * A209662 A209663 A209664
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KEYWORD
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sign,frac,mult
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AUTHOR
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Omar E. Pol, Mar 15 2012
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EXTENSIONS
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Formula in sequence name from M. F. Hasler, Apr 16 2012
a(34) corrected by Ray Chandler, Mar 19 2016
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STATUS
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approved
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