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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.
10
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
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.
Sequence in context: A178659 A268064 A077011 * A370819 A055789 A238891
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 05 2014
STATUS
approved