A128305 a(n) is the smallest m such that g(m) is divisible by prime(n), where g is Landau's function A000793.

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

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

Adjacent sequences: A128302 A128303 A128304 * A128306 A128307 A128308

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