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

Author

Anthony C Robin, May 04 2007

Keywords

• nonn

Examples

			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.
		

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).

Crossrefs

Cf. A000793.

Programs

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 *)

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