

A103332


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


1



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
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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



