A344038 - OEIS

%I #25 Jun 13 2021 13:36:36

%S 1,983583,983029267047,982960635742968103,982953384128772770413831,

%T 982952672223441253533233827367,982952600027678075050509511271466303,

%U 982952593055042000417993486008754893529583,982952592342881094406730790044111038427637071855

%N 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).

%H Chai Wah Wu, <a href="/A344038/b344038.txt">Table of n, a(n) for n = 0..15</a>

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

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

%o (Python)

%o from labmath import mobius

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

%o (PARI) a(n)={sum(k=1, 10^n+1, moebius(k)*(10^n\k)^6)} \\ _Andrew Howroyd_, May 08 2021

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

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

%Y Related counts of k-tuples:

%Y pairs: A018805, A342632, A342586;

%Y triples: A071778, A342935, A342841;

%Y quadruples: A082540, A343527, A343193;

%Y 5-tuples: A343282;

%Y 6-tuples: A343978, A344038. - _N. J. A. Sloane_, Jun 13 2021

%K nonn,less

%O 0,2

%A _Karl-Heinz Hofmann_, May 07 2021

%E Edited by _N. J. A. Sloane_, Jun 13 2021