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 A343193 Number of ordered quadruples (w, x, y, z) with gcd(w, x, y, z) = 1 and 1 <= {w, x, y, z} <= 10^n. 7
 1, 9279, 92434863, 923988964495, 9239427676877311, 92393887177379735327, 923938441006918271400831, 9239384074081430755652624559, 92393840333765561759423951663423, 923938402972369921481535120722882015 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES Joachim von zur Gathen and Jürgen Gerhard, Modern Computer Algebra, Cambridge University Press, Second Edition 2003, pp. 53-54. LINKS Chai Wah Wu, Table of n, a(n) for n = 0..15 FORMULA Lim_{n->infinity} a(n)/10^(4*n) = 1/zeta(4) = A215267 = 90/Pi^4. a(n) = A082540(10^n). EXAMPLE (1,2,2,3) is counted, but (2,4,4,6) is not, because gcd = 2. For n=1, the size of the division tesseract matrix is 10 X 10 X 10 X 10: . o------------x(w=10)------------o /|. ./ | / |. ./ | / |. ./ | / |. ./ | / |. z(w=10) | / |. . / | / |. . / | / |. . / y(w=10) o------------------------------.o | |\ /|¯¯¯¯¯¯x(w=1)¯¯¯¯¯¯/. | | | w / | /.| | | | \ z(w=1)| /. | | | | \ / |y(w=1) /. | | | | \/-------------------/. | | | | | | | | | w | sums | | Cube at w = 1 | | | | ----+----- | | 10 X 10 X 10 | _ _| |---------o 1 | 1000 | | contains | / | / 2 | 875 | | 1000 | / | / 3 | 973 | | completely | / | / 4 | 875 | | reduced fractions | / | / 5 | 992 | | |/ | / 6 | 849 | /------------------- \ | / 7 | 999 | / \ | / 8 | 875 | w w | / 9 | 973 | / \ | / 10 | 868 | / \ |/ ----+----- o -------------------------------o sum for a(1) | 9279 PROG (Python) from labmath import mobius def A343193(n): return sum(mobius(k)*(10**n//k)**4 for k in range(1, 10**n+1)) CROSSREFS Cf. A215267, A013662, A082540, A342841 (3D), A342586 (2D). Related counts of k-tuples: pairs: A018805, A342632, A342586; triples: A071778, A342935, A342841; quadruples: A082540, A343527, A343193; 5-tuples: A343282; 6-tuples: A343978, A344038. - N. J. A. Sloane, Jun 13 2021 Sequence in context: A013900 A100696 A225024 * A237401 A345594 A345852 Adjacent sequences: A343190 A343191 A343192 * A343194 A343195 A343196 KEYWORD nonn AUTHOR Karl-Heinz Hofmann, Apr 07 2021 EXTENSIONS Edited by N. J. A. Sloane, Jun 13 2021 STATUS approved

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Last modified May 24 12:58 EDT 2024. Contains 372773 sequences. (Running on oeis4.)