A259941 Smallest Product_{i:lambda} prime(i) for any complete partition lambda of n.

1, 2, 4, 6, 12, 18, 30, 42, 84, 126, 198, 234, 390, 510, 714, 798, 1596, 1932, 2898, 3654, 5382, 6138, 7254, 8658, 14430, 15990, 20910, 21930, 30702, 33558, 37506, 42294, 84588, 94164, 113988, 117852, 176778, 194166, 244818, 259434, 382122, 392886, 448074

Offset: 0

Author

Alois P. Heinz, Jul 09 2015

Keywords

• nonn

Comments

A complete partition of n contains at least one partition for any k in {0,...,n}. See also A126796.

Examples

			For n=4 there are 2 complete partitions: [2,1,1], and [1,1,1,1], their encodings as Product_{i:lambda} prime(i) give 12, 16, respectively.  The smallest value is a(4) = 12.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Column k=1 of A258118.

Cf. A126796, A259939.

Programs

Maple

b:= proc(n, i) option remember; `if`(i<2, 2^n,
      `if`(n<2*i-1, b(n, iquo(n+1, 2)), min(
       b(n, i-1), b(n-i, i)*ithprime(i))))
    end:
a:= n-> b(n, iquo(n+1, 2)):
seq(a(n), n=0..60);

Mathematica

b[n_, i_] := b[n, i] = If[i<2, 2^n, If[n<2*i-1, b[n, Quotient[n+1, 2]], Min[b[n, i-1], b[n-i, i]*Prime[i]]]]; a[n_] := b[n, Quotient[n+1, 2]]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Jan 15 2016, after Alois P. Heinz *)

Formula

a(n) = A258118(n,1).