A062792 Moebius transform of primorial numbers.

2, 4, 28, 204, 2308, 29996, 510508, 9699480, 223092840, 6469690916, 200560490128, 7420738104576, 304250263527208, 13082761331159516, 614889782588489072, 32589158477180345040, 1922760350154212639068, 117288381359406747860400, 7858321551080267055879088

Offset

1,1

Links

Table of n, a(n) for n=1..19.

Formula

a(n) = Sum_{d|n} f(n/d)*mu(d), where f(n) = A002110(n).

Example

For n=3, a(3) = moebius(1)*primorial(3) + moebius(3)*primorial(1) = 30*1 + 2*(-1) = 30 - 28 = 2.

Mathematica

a[n_] := DivisorSum[n, Product[Prime[i], {i, 1, #}] * MoebiusMu[n/#] &]; Array[a, 17] (* Amiram Eldar, Aug 22 2023 *)

Prog

(PARI) primorial(n) = prod(i=1, n, prime(i));
a(n) = sumdiv(n, d, moebius(d)*primorial(n/d)); \\ Michel Marcus, Apr 05 2014

Crossrefs

Cf. A002110, A008683.

Sequence in context: A259134 A117443 A095858 * A102692 A292184 A248872

Adjacent sequences: A062789 A062790 A062791 * A062793 A062794 A062795

Keyword

nonn

Author

Labos Elemer, Jul 19 2001

Extensions

a(18)-a(19) from Amiram Eldar, Aug 22 2023

Status

approved