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A128305 a(n) is the smallest m such that g(m) is divisible by prime(n), where g is Landau's function A000793. 4
2, 3, 8, 14, 27, 32, 57, 62, 93, 118, 128, 178, 213, 215, 297, 346, 399, 429, 519, 510, 586, 687, 780, 920, 946, 1033, 1106, 1128, 1209, 1192, 1614, 1618, 1788, 1790, 1989, 1987, 2269, 2497, 2271, 2883, 2984, 2986, 3336, 3229, 3579, 3704, 4142, 4367, 4371 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Alois P. Heinz and Giovanni Resta, Table of n, a(n) for n = 1..750 (first 70 terms from Alois P. Heinz)
Jean-Pierre Massias, Jean-Louis Nicolas, Guy Robin, Effective bounds for the maximal order of an element in the symmetric group, Math. Comp. 53 (1989), no. 188, 665--678. MR0979940 (90e:11139).
EXAMPLE
g(k) for k < 14 is not divisible by prime(4) = 7; g(14) = 84 = 7*12. Hence a(4) = 14.
g(k) for k < 32 is not divisible by prime(6) = 13; g(32) = 5460 = 13*420. Hence a(6) = 32.
MATHEMATICA
b[n_, i_] := b[n, i] = Module[{p}, p = If[i < 1, 1, Prime[i]]; If[n == 0 || i < 1, 1, Max[b[n, i - 1], Table[p^j*b[n - p^j, i - 1], {j, 1, Log[p, n] // Floor}]]]];
g[n_] := g[n] = b[n, If[n < 8, 3, PrimePi[Ceiling[1.328*Sqrt[n*Log[n] // Floor]]]]];
a[n_] := For[p = Prime[n]; m = 2, True, m++, If[Divisible[g[m], p], Print[n, " ", m]; Return[m]]];
Array[a, 100] (* Jean-François Alcover, Feb 19 2020, after Alois P. Heinz in A000793 *)
CROSSREFS
Cf. A000793.
Sequence in context: A247124 A171237 A173149 * A328881 A298349 A298343
KEYWORD
nonn
AUTHOR
Anthony C Robin, May 04 2007
EXTENSIONS
Edited, a(6) inserted and a(12) to a(23) added by Klaus Brockhaus, May 07 2007
a(24)-a(70) from Alois P. Heinz, Feb 16 2013
STATUS
approved

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Last modified April 23 11:19 EDT 2024. Contains 371910 sequences. (Running on oeis4.)