A343282 - OEIS

%I #31 Jun 13 2021 13:36:07

%S 1,96601,9645718621,964407482028001,96438925911789115351,

%T 9643875373658964992585011,964387358678775616636890654841,

%U 96438734235127451288511508421855851,9643873406165059293451290072800801506621

%N 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 Joachim von zur Gathen and Jürgen Gerhard, Modern Computer Algebra, Cambridge University Press, Second Edition 2003, pp. 53-54.

%H Chai Wah Wu, <a href="/A343282/b343282.txt">Table of n, a(n) for n = 0..15</a>

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

%F a(n) = A082544(10^n). - _Chai Wah Wu_, Apr 11 2021

%o (Python)

%o from labmath import mobius

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

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

%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

%O 0,2

%A _Karl-Heinz Hofmann_, Apr 10 2021

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