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Max[p1^b1] over all sorted multiplicative partitions of n! of length n.
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%I #8 Apr 02 2015 04:07:26

%S 2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,8,8,

%T 8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,11,11,11,11,11,11,11,11,

%U 11,11,11,11,13,13,13,13,13,13,13,13,13,13,13,13,13,16,16,16,16,16,16,16

%N Max[p1^b1] over all sorted multiplicative partitions of n! of length n.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Alladi-GrinsteadConstant.html">Alladi-Grinstead Constant</a>

%e 6! = 2*2*2*2*5*9 = 2*2*3*3*4*5, the smallest terms of which are 2 and 2, so a(6)=Max[2,2]=2.

%o (PARI) works(n, m) = local(f, s, l, p, x); f = factor(n!); s = 0; l = matsize(f)[1]; for (i = 1, l, p = f[i, 1]; x = 1; while (p^x < m, x++); s += f[i, 2]\x; if (f[i, 2] < x, return(0))); s >= n; a(n) = local(f, m); f = factor(n); m = 2; while (works(n, m), m++); m - 1 \\ _David Wasserman_, Jan 31 2005

%Y Cf. A085288, A085289, A085291.

%Y Cf. A103332.

%K nonn

%O 4,1

%A _Eric W. Weisstein_, Jun 23 2003

%E More terms from _David Wasserman_, Jan 31 2005