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 A343978 Number of ordered 6-tuples (a,b,c,d,e,f) with gcd(a,b,c,d,e,f)=1 (1<= {a,b,c,d,e,f} <= n). 9
 1, 63, 727, 4031, 15559, 45863, 116855, 257983, 526615, 983583, 1755143, 2935231, 4776055, 7407727, 11256623, 16498719, 23859071, 33434063, 46467719, 62949975, 84644439, 111486599, 146142583, 187854119, 240880239, 303814503, 382049919, 473813703, 586746719 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES Joachim von zur Gathen and Jürgen Gerhard, Modern Computer Algebra, Cambridge University Press, Second Edition 2003, pp. 53-54. LINKS Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000 Joachim von zur Gathen and Jürgen Gerhard, Extract from "3.4. (Non-)Uniqueness of the gcd" chapter, Modern Computer Algebra, Cambridge University Press, Second Edition 2003, pp. 53-54. FORMULA a(n) = Sum_{k=1..n} mu(k)*floor(n/k)^6. Lim_{n->infinity} a(n)/n^6 = 1/zeta(6) = A343359 = 945/Pi^6. PROG (Python) from labmath import mobius def A343978(n): return sum(mobius(k)*(n//k)**6 for k in range(1, n+1)) (PARI) a(n)={sum(k=1, n+1, moebius(k)*(n\k)^6)} \\ Andrew Howroyd, May 08 2021 (Python) from functools import lru_cache @lru_cache(maxsize=None) def A343978(n): if n == 0: return 0 c, j, k1 = 1, 2, n//2 while k1 > 1: j2 = n//k1 + 1 c += (j2-j)*A343978(k1) j, k1 = j2, n//j2 return n*(n**5-1)-c+j # Chai Wah Wu, May 17 2021 CROSSREFS Cf. A343359, A013664, A018805, A071778, A082540, A082544. Cf. A342632, A342586, A342935, A342841, A343527, A343193. Sequence in context: A198399 A221968 A115152 * A284953 A069091 A123866 Adjacent sequences: A343975 A343976 A343977 * A343979 A343980 A343981 KEYWORD nonn,less AUTHOR Karl-Heinz Hofmann, May 06 2021 EXTENSIONS Edited by N. J. A. Sloane, Jun 13 2021 STATUS approved

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Last modified September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)