A340795 a(n) is the number of divisors of n that are Brazilian.

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.

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Wikipédia, Nombre brésilien (in French).

Index entries for sequences related to Brazilian numbers.

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

Crossrefs

Cf. A085104, A125134, A220627, A308851, A340796, A340797, A341057, A341058.

Sequence in context: A077402 A287418 A125925 * A137853 A213890 A226460

Adjacent sequences: A340792 A340793 A340794 * A340796 A340797 A340798

Keyword

nonn,base

Author

Bernard Schott, Jan 21 2021

Status

approved