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A308851 Numbers >= 2 whose all divisors > 1 are Brazilian. 7
7, 13, 31, 43, 73, 91, 127, 157, 211, 217, 241, 301, 307, 403, 421, 463, 511, 559, 601, 757, 889, 949, 1093, 1099, 1123, 1333, 1477, 1483, 1651, 1687, 1723, 2041, 2149, 2263, 2551, 2743, 2801, 2821, 2947, 2971, 3133, 3139, 3241, 3307, 3541, 3907, 3913, 3937 (list; graph; refs; listen; history; text; internal format)
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

Amiram Eldar, Table of n, a(n) for n = 1..1000

Index entries for sequences related to Brazilian numbers

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

Cf. A085104 (subsequence), A125134.

Similar with even numbers: A000079, with odd numbers: A005408, with palindromes: A062687, with repdigits: A190217.

Sequence in context: A343302 A110912 A240680 * A298027 A085104 A162652

Adjacent sequences:  A308848 A308849 A308850 * A308852 A308853 A308854

KEYWORD

nonn

AUTHOR

Bernard Schott, Jun 28 2019

STATUS

approved

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Last modified April 15 08:18 EDT 2021. Contains 342977 sequences. (Running on oeis4.)