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A259941 Smallest Product_{i:lambda} prime(i) for any complete partition lambda of n. 3


%S 1,2,4,6,12,18,30,42,84,126,198,234,390,510,714,798,1596,1932,2898,

%T 3654,5382,6138,7254,8658,14430,15990,20910,21930,30702,33558,37506,

%U 42294,84588,94164,113988,117852,176778,194166,244818,259434,382122,392886,448074

%N Smallest Product_{i:lambda} prime(i) for any complete partition lambda of n.

%C A complete partition of n contains at least one partition for any k in {0,...,n}. See also A126796.

%H Alois P. Heinz, <a href="/A259941/b259941.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A258118(n,1).

%e 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.

%p b:= proc(n, i) option remember; `if`(i<2, 2^n,

%p `if`(n<2*i-1, b(n, iquo(n+1, 2)), min(

%p b(n, i-1), b(n-i, i)*ithprime(i))))

%p end:

%p a:= n-> b(n, iquo(n+1, 2)):

%p seq(a(n), n=0..60);

%t 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-Fran├žois Alcover_, Jan 15 2016, after _Alois P. Heinz_ *)

%Y Column k=1 of A258118.

%Y Cf. A126796, A259939.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Jul 09 2015

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Last modified October 20 22:22 EDT 2021. Contains 348119 sequences. (Running on oeis4.)