A338474 - OEIS

%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