OFFSET
1,1
COMMENTS
The terms of this sequence are the Brazilian primes and the products of two or more distinct Brazilian primes.
There are no even numbers because 2 is not Brazilian.
LINKS
EXAMPLE
91 is a term because all divisors of 91 that are > 1: {7, 13, 91} are Brazilian numbers with 7 = 111_2, 13 = 111_3 and 91 = 77_12.
MATHEMATICA
brazQ[n_] := Block[{k, b, ok}, If[FindInstance[k (1 + b) == n && 1 < b < n - 1 && 0 < k < b, {k, b}, Integers] != {}, True, b = 2; ok = False; While[1 + b + b^2 <= n && ! ok, ok = Length@ Union@ IntegerDigits[n, b++] == 1]; ok]]; Select[ Range[3, 4000, 2], AllTrue[ Rest@ Divisors@ #, brazQ] &] (* Giovanni Resta, Jun 29 2019 *)
max = 5000; fQ[n_] := Module[{b = 2, found = False}, While[b < n - 1 && Length[Union[IntegerDigits[n, b]]] > 1, b++]; b < n - 1]; A125134 = Select[Range[4, max], fQ]; Select[Range[2, max], Intersection[A125134, Rest[Divisors[#]]] == Rest[Divisors[#]] &] (* Vaclav Kotesovec, Jun 29 2019, using a subroutine from T. D. Noe *)
PROG
(PARI) isb(n) = for(b=2, n-2, d=digits(n, b); if(vecmin(d)==vecmax(d), return(1)));
isok(n) = {fordiv(n, d, if ((d>1) && ! isb(d), return (0)); ); return (1); } \\ Michel Marcus, Jun 29 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Jun 28 2019
STATUS
approved