OFFSET
0,2
COMMENTS
A complete partition of n contains at least one partition for any k in {0,...,n}. See also A126796.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = A258118(n,1).
EXAMPLE
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.
MAPLE
b:= proc(n, i) option remember; `if`(i<2, 2^n,
`if`(n<2*i-1, b(n, iquo(n+1, 2)), min(
b(n, i-1), b(n-i, i)*ithprime(i))))
end:
a:= n-> b(n, iquo(n+1, 2)):
seq(a(n), n=0..60);
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 09 2015
STATUS
approved