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 A209662 a(n) = (-1)^A083025(n)*n. 5
 1, 2, 3, 4, -5, 6, 7, 8, 9, -10, 11, 12, -13, 14, -15, 16, -17, 18, 19, -20, 21, 22, 23, 24, 25, -26, 27, 28, -29, -30, 31, 32, 33, -34, -35, 36, -37, 38, -39, -40, -41, 42, 43, 44, -45, 46, 47, 48, 49, 50, -51, -52, -53, 54, -55, 56, 57, -58, 59, -60, -61, 62, 63, 64, 65 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also denominators of an infinite series which is equal to pi, if the numerators are 1, 1, 1,..., 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 arises from an infinite series due to Leonhard Euler which is given by: 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... For another version see A209661. a(n) = -n if n has an odd number of prime factors of the form 4k+1 (counted with multiplicity), else a(n) = n. -  M. F. Hasler, Apr 15 2012 Completely multiplicative because A209661 is. - Andrew Howroyd, Aug 04 2018 REFERENCES L. Euler, Introductio in analysin infinitorum, 1748. LINKS Ray Chandler, Table of n, a(n) for n = 1..10000 FORMULA a(n) = n*A209661(n). EXAMPLE For n = 10 we have that the 10th row of triangle A207338 is [2, -5] therefore a(10) = 2*(-5) = -10. PROG (PARI) a(n)={my(f=factor(n)); 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. Numerators are in A000012. Absolute values give A000027. Cf. A000796, A002144, A002145, A002808, A083025, A207338, A209661, A209921, A209922. Sequence in context: A001489 A038608 A105811 * A272813 A258070 A258071 Adjacent sequences:  A209659 A209660 A209661 * A209663 A209664 A209665 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 March 24 19:48 EDT 2019. Contains 321448 sequences. (Running on oeis4.)