

A085290


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


4



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
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OFFSET

4,1


LINKS

Table of n, a(n) for n=4..91.
Eric Weisstein's World of Mathematics, AlladiGrinstead Constant


EXAMPLE

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.


PROG

(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


CROSSREFS

Cf. A085288, A085289, A085291.
Cf. A103332.
Sequence in context: A059396 A108602 A305025 * A108611 A133875 A104355
Adjacent sequences: A085287 A085288 A085289 * A085291 A085292 A085293


KEYWORD

nonn


AUTHOR

Eric W. Weisstein, Jun 23 2003


EXTENSIONS

More terms from David Wasserman, Jan 31 2005


STATUS

approved



