A085290 Max[p1^b1] over all sorted multiplicative partitions of n! of length n.

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, 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, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 16, 16, 16, 16, 16, 16, 16

Offset: 4

Author

Eric W. Weisstein, Jun 23 2003

Keywords

• nonn

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Alladi-Grinstead Constant

Crossrefs

Cf. A085288, A085289, A085291.

Cf. A103332.

Programs

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

Extensions

More terms from David Wasserman, Jan 31 2005