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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
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
Related counts of k-tuples:
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
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.)