A341058 Numbers that have only one divisor that is Brazilian.

7, 8, 10, 12, 13, 15, 18, 22, 27, 31, 33, 34, 38, 43, 46, 49, 51, 55, 57, 58, 69, 73, 74, 82, 85, 87, 94, 95, 106, 111, 115, 118, 121, 122, 123, 125, 127, 134, 141, 142, 145, 157, 158, 159, 166, 169, 177, 178, 183, 185, 187, 194, 201, 202, 205, 206, 209, 211, 213, 214, 218

Offset

1,1

Comments

m is a term iff m is a Brazilian prime (A085104), or m is the square of a Brazilian prime, or m = 121, the only square of prime that is Brazilian, or m = p*q >= 10 with p>q are non-Brazilian primes, or m is the cube of a Brazilian prime, or m = 12 or 18 (see corresponding examples).

Links

Table of n, a(n) for n=1..61.

Formula

A340795(a(n)) = 1.

Example

One example for each type of terms that has k divisors:
-> k=2: 7 is a Brazilian prime, hence 7 = 111_2  is a term.
-> k=3: 169 has three divisors {1, 13, 169} and 13 = 111_3 is the only divisor of 169 that is Brazilian, hence 169 is a term.
-> k=3: 121 has three divisors {1, 11, 121} and 121 = 11111_3, hence, 121 that is the only square of prime that is Brazilian, is a term.
-> k=4: 34 has four divisors {1, 2, 17, 34} and 34 = 22_16  is the only divisor of 34 that is Brazilian, hence 34 is a term.
-> k=4: 27 has four divisors {1, 3, 9, 27} and 27 = 33_8 is the only divisor of 27 that is Brazilian, hence 27 is a term.
-> k=6: only two cases: 12 and 18, these integers have each 6 divisors and only 12 = 22_5 and 18 = 33_5 are Brazilian.

Mathematica

brazQ[n_] := Module[{b = 2, found = False}, While[b < n - 1 && Length @ Union[IntegerDigits[n, b]] > 1, b++]; b < n - 1]; Select[Range[200], DivisorSum[#, 1 &, brazQ[#1] &] == 1 &] (* Amiram Eldar, Feb 16 2021 *)

Crossrefs

Cf. A125134, A220627, A308851, A340795, A341057.

Subsequence: A085104.

Sequence in context: A125134 A169876 A288783 * A120175 A291668 A175222

Adjacent sequences: A341055 A341056 A341057 * A341059 A341060 A341061

Keyword

nonn,base

Author

Bernard Schott, Feb 15 2021

Status

approved