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A326708 Non-Brazilian squares of primes.

%I A326708 #42 Mar 03 2020 05:52:10
%S A326708 4,9,25,49,169,289,361,529,841,961,1369,1681,1849,2209,2809,3481,3721,
%T A326708 4489,5041,5329,6241,6889,7921,9409,10201,10609,11449,11881,12769,
%U A326708 16129,17161,18769,19321,22201,22801,24649,26569,27889,29929,32041,32761
%N A326708 Non-Brazilian squares of primes.
%C A326708 This sequence is a subsequence of A326707.
%C A326708 For these terms, we have the relations beta'(p^2) = beta"(p^2) = beta(p^2) = (tau(p^2) - 3)/2 = 0.
%C A326708 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.
%C A326708 The corresponding square roots are: 2, 3, 5, 7, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, ...
%H A326708 Bernard Schott, <a href="/A326707/a326707.pdf">Array relations beta = f(tau) for squares</a>
%H A326708 Wikipédia, <a href="https://fr.wikipedia.org/wiki/121_(nombre)">121 (nombre)</a> (in French)
%H A326708 Wikipédia, <a href="https://fr.wikipedia.org/wiki/Nombre_br%C3%A9silien">Nombre brésilien</a> (in French)
%H A326708 <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Br#Brazilian_numbers">Index entries for sequences related to Brazilian numbers</a>
%e A326708 49 = 7^2 is not Brazilian, so beta(49) = 0 with tau(49) = 3.
%t A326708 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 *)
%Y A326708 Cf. A190300.
%Y A326708 Subsequence of A000290 and of A220570 and of A190300.
%Y A326708 Intersection of A001248 and A326707.
%K A326708 nonn,base
%O A326708 1,1
%A A326708 _Bernard Schott_, Aug 26 2019