A340796 - OEIS

%I #37 Jul 03 2022 04:51:30

%S 1,7,14,24,40,48,60,84,140,144,120,168,252,700,240,336,560,360,420,

%T 672,1120,2304,960,720,1008,1080,840,2184,1800,1260,2016,5376,8960,

%U 2160,1680,2880,4032,3600,7056,19600,3960,2520,3360,6480,9072,9900,6300,11520,16128

%N a(n) is the smallest number with exactly n divisors that are Brazilian.

%C Primes can be partitioned into Brazilian primes and non-Brazilian primes. If two distinct primes each larger than 11 are in the same category then the larger one has a multiplicity that is smaller than or equal to that of the smaller prime. - _David A. Corneth_, Jan 24 2021

%H David A. Corneth, <a href="/A340796/b340796.txt">Table of n, a(n) for n = 0..427</a>

%H David A. Corneth, <a href="/A340796/a340796.gp.txt">More terms</a>

%H Wikipédia, <a href="https://fr.wikipedia.org/wiki/Nombre_br%C3%A9silien">Nombre brésilien</a> (in French).

%H <a href="/index/Br#Brazilian_numbers">Index entries for sequences related to Brazilian numbers</a>.

%e Of the eight divisors of 24, three are Brazilian numbers: 8, 12 and 24, and there is no smaller number with three Brazilian divisors, hence a(3) = 24.

%t brazQ[n_] := Module[{b = 2, found = False}, While[b < n - 1 && Length[Union[IntegerDigits[n, b]]] > 1, b++]; b < n - 1]; d[n_] := DivisorSum[n, 1 &, brazQ[#] &]; m = 30; s = Table[0, {m}]; c = 0; n = 1; While[c < m, i = d[n]; If[i < m && s[[i + 1]] == 0, c++; s[[i + 1]] = n]; n++]; s (* _Amiram Eldar_, Jan 21 2021 *)

%o (PARI) isokb(n) = for(b=2, n-2, d=digits(n, b); if(vecmin(d)==vecmax(d), return(1))); \\ A125134

%o isok(k, n) = sumdiv(k, d, isokb(d)) == n;

%o a(n) = my(k=1); while (!isok(k, n), k++); k; \\ _Michel Marcus_, Jan 23 2021

%Y Cf. A085104, A125134, A190300, A220570, A308851, A340795, A340797.

%Y Similar with: A087997 (palindromes), A333456 (Niven), A335038 (Zuckerman).

%K nonn,base

%O 0,2

%A _Bernard Schott_, Jan 21 2021

%E More terms from _Amiram Eldar_, Jan 21 2021