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%I #22 Feb 19 2020 10:48:23
%S 2,3,8,14,27,32,57,62,93,118,128,178,213,215,297,346,399,429,519,510,
%T 586,687,780,920,946,1033,1106,1128,1209,1192,1614,1618,1788,1790,
%U 1989,1987,2269,2497,2271,2883,2984,2986,3336,3229,3579,3704,4142,4367,4371
%N a(n) is the smallest m such that g(m) is divisible by prime(n), where g is Landau's function A000793.
%H Alois P. Heinz and Giovanni Resta, <a href="/A128305/b128305.txt">Table of n, a(n) for n = 1..750</a> (first 70 terms from Alois P. Heinz)
%H Jean-Pierre Massias, Jean-Louis Nicolas, Guy Robin, <a href="https://doi.org/10.1090/S0025-5718-1989-0979940-4">Effective bounds for the maximal order of an element in the symmetric group</a>, Math. Comp. 53 (1989), no. 188, 665--678. MR0979940 (90e:11139).
%e g(k) for k < 14 is not divisible by prime(4) = 7; g(14) = 84 = 7*12. Hence a(4) = 14.
%e g(k) for k < 32 is not divisible by prime(6) = 13; g(32) = 5460 = 13*420. Hence a(6) = 32.
%t 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}]]]];
%t g[n_] := g[n] = b[n, If[n < 8, 3, PrimePi[Ceiling[1.328*Sqrt[n*Log[n] // Floor]]]]];
%t a[n_] := For[p = Prime[n]; m = 2, True, m++, If[Divisible[g[m], p], Print[n, " ", m]; Return[m]]];
%t Array[a, 100] (* _Jean-François Alcover_, Feb 19 2020, after _Alois P. Heinz_ in A000793 *)
%Y Cf. A000793.
%K nonn
%O 1,1
%A _Anthony C Robin_, May 04 2007
%E Edited, a(6) inserted and a(12) to a(23) added by _Klaus Brockhaus_, May 07 2007
%E a(24)-a(70) from _Alois P. Heinz_, Feb 16 2013
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