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%I #14 Sep 08 2022 08:46:25
%S 1,8,18,338,462,542,638,660,918,858,924,1260,1140,1122,1428,1326,1740,
%T 1710,2520,2070,1938,3150,3330,27342,27810,29190,30600,35754,32700,
%U 31710,35310,32760,35952,35790,35910,39450,40950,41160,39060,45990,40680,42510,44520
%N a(n) is the smallest number that can be partitioned into n ways as the sum of two brilliant numbers (A078972).
%C Except for 1, all terms are even numbers.
%e 8 = 4 + 4 = A078972(1) + A078972(1);
%e 18 = 4 + 14 = A078972(1) + A078972(5) and 18 = 9 + 9 = A078972(3) + A078972(3).
%e 18 = 15 + 323 = A078972(6) + A078972(22), 338 = 49 + 289 = A078972(10) + A078972(19) and 338 = 169 + 169 = A078972(13) + A078972(13).
%t 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 *)
%o (Magma) f:=Factorisation; brnumber:=func<n|#Divisors(n) eq 3 or &+[d[2]: d in f(n)] eq 2 and #Intseq(f(n)[1][1]) eq #Intseq(Factorization(n)[2][1])>; 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;
%Y Cf. A078972, A100592, A338473.
%K nonn,base
%O 0,2
%A _Marius A. Burtea_, Nov 02 2020
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