%I
%S 7,8,10,12,13,14,16,20,22,27,33,34,35,38,39,43,46,51,55,58,65,69,73,
%T 74,77,81,82,87,94,95,106,115,118,119,121,122,123,125,127,134,141,142,
%U 143,145
%N Brazilian numbers which have only one Brazilian representation.
%C These numbers could be called 1Brazilian numbers.
%C The smallest number of this sequence is 7 = 111_2 which is also the smallest Brazilian number (A125134) and so the smallest Brazilian prime (A085104).
%C a(2) = 8 is the smallest composite Brazilian number and so the smallest even composite Brazilian with 8 = 22_3 (A220571).
%C a(10) = 27 is the smallest odd composite Brazilian in this sequence because 27 = 33_8 but 15 is the smallest odd composite Brazilian with 15 = 1111_2 = 33_4 so with two representations.
%C 121 is the only square of prime which is Brazilian with 121 = 11111_3.
%C In this sequence, there are:
%C 1) The Brazilian primes and the lone square prime 121 which are all repunits in a base >= 2 with a string of at least three 1's.
%C 2) The composite numbers which are such that n = a * b = (aa)_(b1) with 1 < a < b1 with only one such product a * b.
%D D. Lignon, Dictionnaire de (presque) tous les nombres entiers, Ellipses, 2012, page 420.
%H Bernard Schott, <a href="/A125134/a125134.pdf">Les nombres brĂ©siliens</a>, Quadrature, no. 76, avriljuin 2010, pages 3038.
%e 13 = 111_3; 127 = 1111111_2.
%e 20 = 2 * 10 = 22_9; 55 = 5 * 11 = 55_10; 69 = 3 * 23 = 33_22.
%t Select[Range@ 145, Function[n, Count[Range[2, n  2], b_ /; SameQ @@ IntegerDigits[n, b]] == 1]] (* _Michael De Vlieger_, Jun 16 2017 *)
%Y Cf. A085104, A125134, A190300, A220570, A220571, A253260, A284758.
%K nonn,base,easy
%O 1,1
%A _Bernard Schott_, Jun 15 2017
