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

1, 2, 3, 6, 10, 15, 30, 42, 70, 110, 210, 330, 462, 770, 1155, 2310, 2730, 4290, 6006, 10010, 15015, 30030, 39270, 46410, 72930, 102102, 170170, 255255, 510510, 570570, 746130, 903210, 1385670, 1939938, 3233230, 4849845, 9699690, 11741730, 14804790, 17160990

Offset: 0

Author

Alois P. Heinz, Sep 05 2014

Keywords

• nonn

Comments

The number of (distinct) prime factors in a(n) is A003056(n) = floor((sqrt(1+8*n)-1)/2).

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..3000

Crossrefs

Last elements of rows of A246867.

Cf. A000009, A003056.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      max(b(n, i-1), `if`(i>n, 0, b(n-i, i-1)*ithprime(i)))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..50);

Mathematica

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 *)

Formula

a(n) = A246867(n,A000009(n)).