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

Author

David Wasserman, Jan 31 2005

Keywords

• nonn
• less

Comments

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

Crossrefs

Cf. A085289, A085290.

Programs

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