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A259941 Smallest Product_{i:lambda} prime(i) for any complete partition lambda of n. 3
1, 2, 4, 6, 12, 18, 30, 42, 84, 126, 198, 234, 390, 510, 714, 798, 1596, 1932, 2898, 3654, 5382, 6138, 7254, 8658, 14430, 15990, 20910, 21930, 30702, 33558, 37506, 42294, 84588, 94164, 113988, 117852, 176778, 194166, 244818, 259434, 382122, 392886, 448074 (list; graph; refs; listen; history; text; internal format)
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

Column k=1 of A258118.

Cf. A126796, A259939.

Sequence in context: A181740 A192224 A167777 * A007436 A052847 A331933

Adjacent sequences:  A259938 A259939 A259940 * A259942 A259943 A259944

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 09 2015

STATUS

approved

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Last modified September 24 06:13 EDT 2021. Contains 347623 sequences. (Running on oeis4.)