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

0,2

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

Last elements of rows of A246867.

Cf. A000009, A003056.

Sequence in context: A178659 A268064 A077011 * A370819 A055789 A238891

Adjacent sequences: A246865 A246866 A246867 * A246869 A246870 A246871

Keyword

nonn

Author

Alois P. Heinz, Sep 05 2014

Status

approved