A051704 Maximal value of products of partitions of n into powers of distinct primes (powers of 1 and 2 excluded).
1, 0, 0, 3, 0, 5, 0, 7, 15, 9, 21, 11, 35, 13, 45, 105, 63, 17, 77, 165, 99, 315, 117, 385, 143, 495, 1155, 693, 1365, 819, 221, 1001, 3465, 1287, 4095, 1309, 5005, 1683, 6435, 15015, 9009, 2431, 8415, 19635, 11781, 45045, 13923, 25935, 17017, 58905, 21879
Offset: 0
Keywords
Examples
a(14)=45 because max{3*11,9*5}=45.
Crossrefs
Cf. A051703.
Programs
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Mathematica
a[n_] := (pp = Reap[ Do[ pk = p^k; If[pk <= n, Sow[pk]], {p, Prime[ Range[2, PrimePi[n]]]}, {k, 1, Ceiling[Log[3, n]]}]][[2, 1]]; sel = Select[ IntegerPartitions[n, All, pp], Length[#] == Length[ Union[#] && !MatchQ[#, {_, x_, _, y_, _} /; GCD[x, y] != 1]] &]; Max[Times @@@ sel]); a[0] = 1; a[1] = a[2] = a[4] = a[6] = 0; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jul 31 2012 *)
Extensions
a(43) (typo?) corrected by Jean-François Alcover, Jul 31 2012