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%I #3 Mar 31 2012 13:20:57
%S 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,
%T 29,29,31,31,31,31,31,31,37,37,37,37,41,41,43,43,43,43,47,47,49,49,49,
%U 49,53,53,53,53,53,53,59,59,61,61,61,61,61,64,67,67,67,67,71,71,73,73,73
%N Min[pn^bn] over all sorted multiplicative partitions of n! of length n.
%C a(n) >= A007917(n); a(n) is a power of some prime p <= n.
%o (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
%Y Cf. A085289, A085290.
%K nonn,less
%O 4,1
%A _David Wasserman_, Jan 31 2005
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