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

4,1

Links

Table of n, a(n) for n=4..91.

Eric Weisstein's World of Mathematics, Alladi-Grinstead 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: A108602 A305025 A363743 * 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