A343282 Number of ordered 5-tuples (v,w, x, y, z) with gcd(v, w, x, y, z) = 1 and 1 <= {v, w, x, y, z} <= 10^n.

1, 96601, 9645718621, 964407482028001, 96438925911789115351, 9643875373658964992585011, 964387358678775616636890654841, 96438734235127451288511508421855851, 9643873406165059293451290072800801506621

Offset: 0

Author

Karl-Heinz Hofmann, Apr 10 2021

Keywords

• nonn

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

Crossrefs

Cf. A082544, A013663, A342586, A342841, A343193.

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

Programs

Python

from labmath import mobius
def A343282(n): return sum(mobius(k)*(10**n//k)**5 for k in range(1, 10**n+1))

Formula

Lim_{n->infinity} a(n)/10^(5*n) = 1/zeta(5) = A343308.

a(n) = A082544(10^n). - Chai Wah Wu, Apr 11 2021

Extensions

Edited by N. J. A. Sloane, Jun 13 2021