|
|
A308851
|
|
Numbers >= 2 all of whose 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
|
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|