A344038 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} <= 10^n).

1, 983583, 983029267047, 982960635742968103, 982953384128772770413831, 982952672223441253533233827367, 982952600027678075050509511271466303, 982952593055042000417993486008754893529583, 982952592342881094406730790044111038427637071855

Offset: 0

Author

Karl-Heinz Hofmann, May 07 2021

Keywords

• nonn
• less

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..15

Crossrefs

Cf. A342586, A342841, A343193, A343282, A343359, A013664.

Cf. A343978, A071778, A018805, A082540, A082544.

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

PARI

a(n)={sum(k=1, 10^n+1, moebius(k)*(10^n\k)^6)} \\ Andrew Howroyd, May 08 2021

Python

from labmath import mobius
def A344038(n): return sum(mobius(k)*(10**n//k)**6 for k in range(1, 10**n+1))

Formula

Lim_{n->infinity} a(n)/10^(6*n) = 1/zeta(6) = A343359 = 945/Pi^4.

a(n) = A343978(10^n).

Extensions

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