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%I #49 May 08 2021 02:26:28
%S 7,13,31,43,73,91,127,157,211,217,241,301,307,403,421,463,511,559,601,
%T 757,889,949,1093,1099,1123,1333,1477,1483,1651,1687,1723,2041,2149,
%U 2263,2551,2743,2801,2821,2947,2971,3133,3139,3241,3307,3541,3907,3913,3937
%N Numbers >= 2 all of whose divisors > 1 are Brazilian.
%C The terms of this sequence are the Brazilian primes and the products of two or more distinct Brazilian primes.
%C There are no even numbers because 2 is not Brazilian.
%H Amiram Eldar, <a href="/A308851/b308851.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Br#Brazilian_numbers">Index entries for sequences related to Brazilian numbers</a>
%e 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.
%t 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 *)
%t 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_ *)
%o (PARI) isb(n) = for(b=2, n-2, d=digits(n, b); if(vecmin(d)==vecmax(d), return(1)));
%o isok(n) = {fordiv(n, d, if ((d>1) && ! isb(d), return (0));); return (1);} \\ _Michel Marcus_, Jun 29 2019
%Y Cf. A085104 (subsequence), A125134.
%Y Similar with even numbers: A000079, with odd numbers: A005408, with palindromes: A062687, with repdigits: A190217.
%K nonn
%O 1,1
%A _Bernard Schott_, Jun 28 2019
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