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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.

%I A343282 #31 Jun 13 2021 13:36:07
%S A343282 1,96601,9645718621,964407482028001,96438925911789115351,
%T A343282 9643875373658964992585011,964387358678775616636890654841,
%U A343282 96438734235127451288511508421855851,9643873406165059293451290072800801506621
%N 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.
%D A343282 Joachim von zur Gathen and Jürgen Gerhard, Modern Computer Algebra, Cambridge University Press, Second Edition 2003, pp. 53-54.
%H A343282 Chai Wah Wu, <a href="/A343282/b343282.txt">Table of n, a(n) for n = 0..15</a>
%F A343282 Lim_{n->infinity} a(n)/10^(5*n) = 1/zeta(5) = A343308.
%F A343282 a(n) = A082544(10^n). - _Chai Wah Wu_, Apr 11 2021
%o A343282 (Python)
%o A343282 from labmath import mobius
%o A343282 def A343282(n): return sum(mobius(k)*(10**n//k)**5 for k in range(1, 10**n+1))
%Y A343282 Cf. A082544, A013663, A342586, A342841, A343193.
%Y A343282 Related counts of k-tuples:
%Y A343282 pairs: A018805, A342632, A342586;
%Y A343282 triples: A071778, A342935, A342841;
%Y A343282 quadruples: A082540, A343527, A343193;
%Y A343282 5-tuples: A343282;
%Y A343282 6-tuples: A343978, A344038. - _N. J. A. Sloane_, Jun 13 2021
%K A343282 nonn
%O A343282 0,2
%A A343282 _Karl-Heinz Hofmann_, Apr 10 2021
%E A343282 Edited by _N. J. A. Sloane_, Jun 13 2021