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

1,2

Comments

See A215474 for the definitions.

Links

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

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).

Example

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

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 *)

Prog

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

Crossrefs

Cf. A215474, A143328.

Sequence in context: A202293 A202294 A029767 * A120056 A125788 A183611

Adjacent sequences: A215472 A215473 A215474 * A215476 A215477 A215478

Keyword

nonn

Author

Peter Luschny, Aug 12 2012

Status

approved