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 A209661 a(n) = (-1)^A083025(n). 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS 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. REFERENCES L. Euler, Introductio in analysin infinitorum, 1748. LINKS Ray Chandler, Table of n, a(n) for n = 1..10000 FORMULA 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 EXAMPLE For n = 10 we have that the 10th row of triangle A207338 is [2, -5] therefore a(10) = 2*(-5)/10 = -1. PROG (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 CROSSREFS 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 KEYWORD sign,frac,mult AUTHOR Omar E. Pol, Mar 15 2012 EXTENSIONS Formula in sequence name from M. F. Hasler, Apr 16 2012 a(34) corrected by Ray Chandler, Mar 19 2016 STATUS approved

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Last modified April 20 23:46 EDT 2021. Contains 343143 sequences. (Running on oeis4.)