A215475 Number of n-ary n-tuples (a_1,...,a_n) such that the string a_1...a_n is preprime.

1, 3, 14, 90, 829, 9695, 141280, 2447592, 49212093, 1125217654, 28823053258, 817378772782, 25417591386199, 859893804621774, 31439503146486552, 1235301513403984512, 51906185332282554369, 2322562816163062723410, 110253678955655801174716, 5534198888175777261628156

Offset: 1

Author

Peter Luschny, Aug 12 2012

Keywords

• nonn

Comments

See A215474 for the definitions.

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..387

Crossrefs

Cf. A215474, A143328.

Programs

Mathematica

a[n_] := Sum[1/j Sum[MoebiusMu[j/d] n^d, {d, Divisors[j]}], {j, n}];
Array[a, 20] (* Jean-François Alcover, Jun 27 2019 *)

PARI

a(n) = sum(j=1, n, sumdiv(j, d, moebius(j/d)*n^d)/j); \\ Michel Marcus, Jun 27 2019

Sage

def A215475(n):
     return add((1/j)*add(moebius(j/d)*n^d for d in divisors(j)) for j in (1..n))
[A215475(n) for n in (1..20)]

Formula

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

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