login
A340795
a(n) is the number of divisors of n that are Brazilian.
5
0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 2, 2, 1, 0, 3, 0, 2, 1, 3, 0, 3, 1, 3, 1, 1, 2, 3, 0, 1, 2, 4, 0, 4, 1, 2, 2, 1, 0, 5, 1, 2, 1, 3, 0, 3, 1, 5, 1, 1, 0, 6, 0, 2, 3, 4, 2, 3, 0, 2, 1, 5, 0, 6, 1, 1, 2, 2, 2, 4, 0, 6, 2, 1, 0, 7, 1, 2, 1, 4, 0, 6
OFFSET
1,14
COMMENTS
The cases a(n) = 0 and a(n) = 1 are respectively detailed in A341057 and A341058.
EXAMPLE
For n = 16, the divisors are 1, 2, 4, 8 and 16. Only 8 = 22_3 and 16 = 22_7 are Brazilian numbers, so a(16) = 2.
For n = 30, the divisors are 1, 2, 3, 5, 6, 10, 15 and 30. Only 10 = 22_4, 15 = 33_4 and 30 = 33_9 are Brazilian numbers, so a(30) = 3.
For n = 49, the divisors are 1, 7 and 49. Only 7 = 111_2 is Brazilian, so a(49) = 1 although 49 that is square of prime <> 121 is not Brazilian.
MATHEMATICA
brazQ[n_] := Module[{b = 2, found = False}, While[b < n - 1 && Length[Union[IntegerDigits[n, b]]] > 1, b++]; b < n - 1]; a[n_] := DivisorSum[n, 1 &, brazQ[#] &]; Array[a, 100] (* Amiram Eldar, Jan 21 2021 *)
PROG
(PARI) isb(n) = for(b=2, n-2, d=digits(n, b); if(vecmin(d)==vecmax(d), return(1))); \\ A125134
a(n) = sumdiv(n, d, isb(d)); \\ Michel Marcus, Jan 24 2021
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Jan 21 2021
STATUS
approved