A220571 Composite numbers that are Brazilian.

8, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100

Offset: 1

Author

Bernard Schott, Dec 16 2012

Keywords

• nonn

Comments

There are just two differences of members with A080257:

1) the term 6 is missing here because 6 is not a Brazilian number.

2) the new term 121 is present although 121 has only 3 divisors, because 121 = 11^2 = 11111_3 is a composite number which is Brazilian. 121 is the lone square of a prime which is Brazilian: Theorem 5, page 37 of Quadrature article in links.

There is an infinity of Brazilian composite numbers (Theorem 1, page 32 of Quadrature article in links: every even number >= 8 is a Brazilian number).

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38; included here with permission from the editors of Quadrature.

Crossrefs

Cf. A125134, A190300.

Programs

Mathematica

Select[Range[4, 10^2], And[CompositeQ@ #, Module[{b = 2, n = #}, While[And[b < n - 1, Length@ Union@ IntegerDigits[n, b] > 1], b++]; b < n - 1]] &] (* Michael De Vlieger, Jul 30 2017, after T. D. Noe at A125134 *)