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A093773
a(n) is the smallest integer at which the value of the "truncated Mertens function" (= A088004) equals the n-th prime number.
4
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).
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 28 2004
STATUS
approved