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A338474
a(n) is the smallest number that can be partitioned into n ways as the sum of two brilliant numbers (A078972).
1
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
0,2
COMMENTS
Except for 1, all terms are even numbers.
EXAMPLE
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).
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 *)
PROG
(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;
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Marius A. Burtea, Nov 02 2020
STATUS
approved