A338474 a(n) is the smallest number that can be partitioned into n ways as the sum of two brilliant numbers (A078972).

1, 8, 18, 338, 462, 542, 638, 660, 918, 858, 924, 1260, 1140, 1122, 1428, 1326, 1740, 1710, 2520, 2070, 1938, 3150, 3330, 27342, 27810, 29190, 30600, 35754, 32700, 31710, 35310, 32760, 35952, 35790, 35910, 39450, 40950, 41160, 39060, 45990, 40680, 42510, 44520

Offset: 0

Author

Marius A. Burtea, Nov 02 2020

Keywords

• nonn
• base

Comments

Except for 1, all terms are even numbers.

Examples

			8 = 4 + 4 = A078972(1) + A078972(1);
18 = 4 + 14 = A078972(1) + A078972(5) and 18 = 9 + 9 = A078972(3) + A078972(3).
18 = 15 + 323 = A078972(6) + A078972(22), 338 = 49 + 289 = A078972(10) + A078972(19) and 338 = 169 + 169 = A078972(13) + A078972(13).
		

Crossrefs

Cf. A078972, A100592, A338473.

Programs

Magma

f:=Factorisation; brnumber:=func; v:=[m:m in [2..50000]|brnumber(m)]; a:=[]; for n in [0..32] do k:=1; while  #RestrictedPartitions(k,2,Set(v)) ne n do k:=k+1; end while ; Append(~a,k); end for; a;

Mathematica

m = 46000; brils = Select[Range[m], (f = FactorInteger[#])[[;; , 2]] == {2} || f[[;; , 2]] == {1, 1} && Equal @@ IntegerLength@f[[;; , 1]] &]; a[n_] := Length[IntegerPartitions[n, {2}, brils]]; mx = 43; s = Table[-1, {mx}]; c = 0; n = 1; While[c < mx, i = a[n] + 1; If[i <= mx && s[[i]] < 0, c++; s[[i]] = n]; n++]; s (* Amiram Eldar, Nov 03 2020 *)