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A246868 Largest number that can be encoded as Product_{i:lambda} prime(i) for a partition lambda of n into distinct parts.

%I A246868 #18 Feb 07 2017 08:28:00
%S A246868 1,2,3,6,10,15,30,42,70,110,210,330,462,770,1155,2310,2730,4290,6006,
%T A246868 10010,15015,30030,39270,46410,72930,102102,170170,255255,510510,
%U A246868 570570,746130,903210,1385670,1939938,3233230,4849845,9699690,11741730,14804790,17160990
%N A246868 Largest number that can be encoded as Product_{i:lambda} prime(i) for a partition lambda of n into distinct parts.
%C A246868 The number of (distinct) prime factors in a(n) is A003056(n) = floor((sqrt(1+8*n)-1)/2).
%H A246868 Alois P. Heinz, <a href="/A246868/b246868.txt">Table of n, a(n) for n = 0..3000</a>
%F A246868 a(n) = A246867(n,A000009(n)).
%e A246868 The partitions of n=5 into distinct parts are {[5], [4,1], [3,2]}, encodings give {prime(5), prime(4)*prime(1), prime(3)*prime(2)} = {11, 7*2, 5*3} = {11, 14, 15}.  So a(5) = max(11,14,15) = 15.
%p A246868 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A246868       max(b(n, i-1), `if`(i>n, 0, b(n-i, i-1)*ithprime(i)))))
%p A246868     end:
%p A246868 a:= n-> b(n$2):
%p A246868 seq(a(n), n=0..50);
%t A246868 b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Max[b[n, i-1], If[i>n, 0, b[n - i, i-1]*Prime[i]]]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Feb 07 2017, translated from Maple *)
%Y A246868 Last elements of rows of A246867.
%Y A246868 Cf. A000009, A003056.
%K A246868 nonn
%O A246868 0,2
%A A246868 _Alois P. Heinz_, Sep 05 2014