A326708 Non-Brazilian squares of primes.

4, 9, 25, 49, 169, 289, 361, 529, 841, 961, 1369, 1681, 1849, 2209, 2809, 3481, 3721, 4489, 5041, 5329, 6241, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12769, 16129, 17161, 18769, 19321, 22201, 22801, 24649, 26569, 27889, 29929, 32041, 32761

Offset

1,1

Comments

This sequence is a subsequence of A326707.

For these terms, we have the relations beta'(p^2) = beta"(p^2) = beta(p^2) = (tau(p^2) - 3)/2 = 0.

This sequence = A001248 \ {121} because 121 is the only known square of a prime that is Brazilian (Wikipédia link); 121 is a solution y^q of the Nagell-Ljunggren equation y^q = (b^m-1)/(b-1) with y = 11, q =2, b = 3, m = 5 (see A208242), hence 121 = 11^2 = (3^5 -1)/2 = 11111_3.

The corresponding square roots are: 2, 3, 5, 7, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, ...

Links

Table of n, a(n) for n=1..41.

Bernard Schott, Array relations beta = f(tau) for squares

Wikipédia, 121 (nombre) (in French)

Wikipédia, Nombre brésilien (in French)

Index entries for sequences related to Brazilian numbers

Example

49 = 7^2 is not Brazilian, so beta(49) = 0 with tau(49) = 3.

Mathematica

brazBases[n_] := Select[Range[2, n - 2], Length[Union[IntegerDigits[n, #]]] == 1 &]; Select[Range[2, 1000], PrimeQ[#^(1/2)]&& brazBases[#] == {} &] (* Metin Sariyar, Sep 05 2019 *)

Crossrefs

Cf. A190300.

Subsequence of A000290 and of A220570 and of A190300.

Intersection of A001248 and A326707.

Sequence in context: A001255 A357754 A133019 * A028866 A146981 A068373

Adjacent sequences: A326705 A326706 A326707 * A326709 A326710 A326711

Keyword

nonn,base

Author

Bernard Schott, Aug 26 2019

Status

approved