A215475 - OEIS

%I #16 Jun 28 2019 04:17:43

%S 1,3,14,90,829,9695,141280,2447592,49212093,1125217654,28823053258,

%T 817378772782,25417591386199,859893804621774,31439503146486552,

%U 1235301513403984512,51906185332282554369,2322562816163062723410,110253678955655801174716,5534198888175777261628156

%N Number of n-ary n-tuples (a_1,...,a_n) such that the string a_1...a_n is preprime.

%C See A215474 for the definitions.

%H Alois P. Heinz, <a href="/A215475/b215475.txt">Table of n, a(n) for n = 1..387</a>

%F a(n) = Sum_{j=1..n} (1/j)*Sum_{d|j} mu(j/d)*n^d.

%F a(n) = A215474(n,n) = A143328(n,n).

%e a(3) = 14 = card{000, 001, 002, 010, 011, 012, 020, 021, 022, 111, 112, 121, 122, 222}.

%t a[n_] := Sum[1/j Sum[MoebiusMu[j/d] n^d, {d, Divisors[j]}], {j, n}];

%t Array[a, 20] (* _Jean-François Alcover_, Jun 27 2019 *)

%o (Sage)

%o def A215475(n):

%o      return add((1/j)*add(moebius(j/d)*n^d for d in divisors(j)) for j in (1..n))

%o [A215475(n) for n in (1..20)]

%o (PARI) a(n) = sum(j=1, n, sumdiv(j, d, moebius(j/d)*n^d)/j); \\ _Michel Marcus_, Jun 27 2019

%Y Cf. A215474, A143328.

%K nonn

%O 1,2

%A _Peter Luschny_, Aug 12 2012