A062792 - OEIS

%I #18 Aug 22 2023 07:59:48

%S 2,4,28,204,2308,29996,510508,9699480,223092840,6469690916,

%T 200560490128,7420738104576,304250263527208,13082761331159516,

%U 614889782588489072,32589158477180345040,1922760350154212639068,117288381359406747860400,7858321551080267055879088

%N Moebius transform of primorial numbers.

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

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

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

%o (PARI) primorial(n) = prod(i=1, n, prime(i));

%o a(n) = sumdiv(n, d, moebius(d)*primorial(n/d)); \\ _Michel Marcus_, Apr 05 2014

%Y Cf. A002110, A008683.

%K nonn

%O 1,1

%A _Labos Elemer_, Jul 19 2001

%E a(18)-a(19) from _Amiram Eldar_, Aug 22 2023