A093773 a(n) is the smallest integer at which the value of the "truncated Mertens function" (= A088004) equals the n-th prime number.

6, 10, 15, 22, 38, 51, 62, 77, 91, 123, 134, 159, 203, 206, 214, 253, 302, 305, 330, 341, 365, 395, 454, 489, 526, 542, 545, 554, 566, 586, 723, 753, 781, 794, 866, 870, 914, 933, 966, 1059, 1138, 1141, 1198, 1202, 1214, 1219, 1293, 1351, 1383, 1387, 1403

Offset: 1

Author

Labos Elemer, Apr 28 2004

Keywords

• nonn

Comments

Truncated Mertens function = summatory Moebius when argument runs through nonprimes. See A088004(n) = A002321(n) + A000720(n).

Crossrefs

Cf. A000720, A002321, A008682, A059071, A088004, A093772.

Programs

Mathematica

mer[x_] :=mer[x]=mer[x-1]+MoebiusMu[x]; mer[0]=0;$RecursionLimit=1000; t=Table[mer[w]+PrimePi[w], {w, 1, 1000}] Table[Min[Flatten[Position[t, Prime[j]]]], {j, 1, 200}]

Formula

a(n) = A093772(prime(n)) = A093772(A000040(n)). Solutions to min{x; A002321(x) + A000720(x) = A000040(n) = prime(n)} = a(n).