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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).

%I A344038 #25 Jun 13 2021 13:36:36
%S A344038 1,983583,983029267047,982960635742968103,982953384128772770413831,
%T A344038 982952672223441253533233827367,982952600027678075050509511271466303,
%U A344038 982952593055042000417993486008754893529583,982952592342881094406730790044111038427637071855
%N 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).
%H A344038 Chai Wah Wu, <a href="/A344038/b344038.txt">Table of n, a(n) for n = 0..15</a>
%F A344038 Lim_{n->infinity} a(n)/10^(6*n) = 1/zeta(6) = A343359 = 945/Pi^4.
%F A344038 a(n) = A343978(10^n).
%o A344038 (Python)
%o A344038 from labmath import mobius
%o A344038 def A344038(n): return sum(mobius(k)*(10**n//k)**6 for k in range(1, 10**n+1))
%o A344038 (PARI) a(n)={sum(k=1, 10^n+1, moebius(k)*(10^n\k)^6)} \\ _Andrew Howroyd_, May 08 2021
%Y A344038 Cf. A342586, A342841, A343193, A343282, A343359, A013664.
%Y A344038 Cf. A343978, A071778, A018805, A082540, A082544.
%Y A344038 Related counts of k-tuples:
%Y A344038 pairs: A018805, A342632, A342586;
%Y A344038 triples: A071778, A342935, A342841;
%Y A344038 quadruples: A082540, A343527, A343193;
%Y A344038 5-tuples: A343282;
%Y A344038 6-tuples: A343978, A344038. - _N. J. A. Sloane_, Jun 13 2021
%K A344038 nonn,less
%O A344038 0,2
%A A344038 _Karl-Heinz Hofmann_, May 07 2021
%E A344038 Edited by _N. J. A. Sloane_, Jun 13 2021