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A343978
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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).
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9
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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
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OFFSET
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1,2
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REFERENCES
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Joachim von zur Gathen and Jürgen Gerhard, Modern Computer Algebra, Cambridge University Press, Second Edition 2003, pp. 53-54.
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LINKS
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FORMULA
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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.
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PROG
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(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)
if n == 0:
return 0
c, j, k1 = 1, 2, n//2
while k1 > 1:
j2 = n//k1 + 1
j, k1 = j2, n//j2
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CROSSREFS
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KEYWORD
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nonn,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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