A103332 Min[pn^bn] over all sorted multiplicative partitions of n! of length n.

3, 5, 5, 7, 7, 8, 8, 11, 11, 13, 13, 13, 13, 17, 17, 19, 19, 19, 19, 23, 23, 25, 25, 25, 25, 29, 29, 31, 31, 31, 31, 31, 31, 37, 37, 37, 37, 41, 41, 43, 43, 43, 43, 47, 47, 49, 49, 49, 49, 53, 53, 53, 53, 53, 53, 59, 59, 61, 61, 61, 61, 61, 64, 67, 67, 67, 67, 71, 71, 73, 73, 73

Offset

4,1

Comments

a(n) >= A007917(n); a(n) is a power of some prime p <= n.

Links

Table of n, a(n) for n=4..75.

Prog

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

Crossrefs

Cf. A085289, A085290.

Sequence in context: A126611 A164019 A307701 * A195796 A279944 A309424

Adjacent sequences: A103329 A103330 A103331 * A103333 A103334 A103335

Keyword

nonn,less

Author

David Wasserman, Jan 31 2005

Status

approved