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

0,4

Links

Table of n, a(n) for n=0..50.

Example

a(14)=45 because max{3*11,9*5}=45.

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 *)

Crossrefs

Cf. A051703.

Sequence in context: A325962 A210451 A239233 * A049689 A227901 A118657

Adjacent sequences: A051701 A051702 A051703 * A051705 A051706 A051707

Keyword

nonn

Author

Vladeta Jovovic

Extensions

a(43) (typo?) corrected by Jean-François Alcover, Jul 31 2012

Status

approved