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

1,1

Comments

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

Links

Table of n, a(n) for n=1..51.

Formula

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

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}]

Crossrefs

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

Sequence in context: A285766 A157344 A332765 * A088708 A174872 A229273

Adjacent sequences: A093770 A093771 A093772 * A093774 A093775 A093776

Keyword

nonn

Author

Labos Elemer, Apr 28 2004

Status

approved