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

%I A259941 #10 Jan 15 2016 14:54:48
%S A259941 1,2,4,6,12,18,30,42,84,126,198,234,390,510,714,798,1596,1932,2898,
%T A259941 3654,5382,6138,7254,8658,14430,15990,20910,21930,30702,33558,37506,
%U A259941 42294,84588,94164,113988,117852,176778,194166,244818,259434,382122,392886,448074
%N A259941 Smallest Product_{i:lambda} prime(i) for any complete partition lambda of n.
%C A259941 A complete partition of n contains at least one partition for any k in {0,...,n}.  See also A126796.
%H A259941 Alois P. Heinz, <a href="/A259941/b259941.txt">Table of n, a(n) for n = 0..10000</a>
%F A259941 a(n) = A258118(n,1).
%e A259941 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.
%p A259941 b:= proc(n, i) option remember; `if`(i<2, 2^n,
%p A259941       `if`(n<2*i-1, b(n, iquo(n+1, 2)), min(
%p A259941        b(n, i-1), b(n-i, i)*ithprime(i))))
%p A259941     end:
%p A259941 a:= n-> b(n, iquo(n+1, 2)):
%p A259941 seq(a(n), n=0..60);
%t A259941 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_ *)
%Y A259941 Column k=1 of A258118.
%Y A259941 Cf. A126796, A259939.
%K A259941 nonn
%O A259941 0,2
%A A259941 _Alois P. Heinz_, Jul 09 2015