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 A089128 Greatest common divisor of n^2-6 and n^2+6. 7
 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The second term of sequences of this type for n=0,1,2... form the sequence 1,2,1,2,1,...in decimal .1212121212... = 4/33 Multiplicative with a(p^e) = GCD(p^e, 6). David W. Wilson Jun 12, 2005. Contribution from Jaroslav Krizek, May 27 2010: (Start) a(n) = denominators of averages of squares of the first n positive integers for n >= 1. a(n) for n >= 1 is periodic sequence with period (1, 2, 3, 2, 1, 6). See A175485 - numerators of averages of squares of the first n positive integers. a(n) = A175485(n) * n / A000330(n). For n = 337 holds: a(n) = 1 and simultaneously A175485(n) is square ( = 38025 = 195^2), i.e. number k = 195 is quadratic mean (root mean square) of first 337 positive integers. There are other such numbers - see A084231 and A084232. Sqrt (A175485(n) / a(n)) for n >= 1 is harmonic mean of the first n positive integers. (End) LINKS Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,0,0,1) FORMULA a(n) = GCD(6, n). David W. Wilson Jun 12, 2005. a(n) = 1 + [2|n] + 2*[3|n] + 2*[6|n] = (15 + 5*(-1)^n + 4*cos(n*Pi/3) + 12*cos(n*2*Pi/3))/6, where [x|y] is 1 if x divides y, 0 otherwise. Mitch Harris Jun 15, 2005. a(n) = (-2*(n mod 6)+(n+1 mod 6)+(n+2 mod 6)+3*(n+5 mod 6))/3 (cf. forms of modular arithmetic of Paolo P. Lava, i.e. see A146094). [From Bruno Berselli, Sep 27 2010] Dirichlet g.f. zeta(s)*(1+1/2^s+2/3^s+2/6^s). G.f. ( -6-x-2*x^2-3*x^3-2*x^4-x^5 ) / ( (x-1)*(1+x)*(1+x+x^2)*(x^2-x+1) ). - R. J. Mathar, Apr 04 2011 a(n) = ((n-1) mod 2 + 1)*( 2*floor(((n-1) mod 3)/2) + 1). [From Gary Detlefs, Dec 28 2011] PROG (PARI) g(n) = for(x=0, n, print1(gcd(x^2-6, x^2+6)", ")) CROSSREFS Sequence in context: A153736 A165070 A164809 * A222215 A106687 A083463 Adjacent sequences:  A089125 A089126 A089127 * A089129 A089130 A089131 KEYWORD easy,nonn,mult AUTHOR Cino Hilliard (hillcino368(AT)gmail.com), Dec 05 2003 STATUS approved

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Last modified May 22 09:43 EDT 2013. Contains 225519 sequences.