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A062792
Moebius transform of primorial numbers.
0
2, 4, 28, 204, 2308, 29996, 510508, 9699480, 223092840, 6469690916, 200560490128, 7420738104576, 304250263527208, 13082761331159516, 614889782588489072, 32589158477180345040, 1922760350154212639068, 117288381359406747860400, 7858321551080267055879088
OFFSET
1,1
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
Sequence in context: A259134 A117443 A095858 * A102692 A292184 A248872
KEYWORD
nonn
AUTHOR
Labos Elemer, Jul 19 2001
EXTENSIONS
a(18)-a(19) from Amiram Eldar, Aug 22 2023
STATUS
approved