This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A232527 #18 Aug 09 2015 16:07:21
%S A232527 1,2,3,5,6,9,10,12,13,14,17,21,22,30,33,34,37,42,46,49,57,58,65,66,69,
%T A232527 70,73,77,78,82,85,90,93,97,102,105,114,117,130,133,138,141,142,145,
%U A232527 154,165,177,190,193,198,205,210,213,217,238,253,258,265,273,282,285,301,310,322,330,333,345,357,385,390
%N A232527 Numbers n such that there are no positive integers m such that m^3 is of the form x^2 + n*y^2 and m is not of the form x^2 + n*y^2.
%C A232527 Equivalently, numbers n such that there are no positive integers m such that m^r is of the form x^2 + n*y^2 and m is not of the form x^2 + n*y^2, for any odd integer r >= 3.
%C A232527 Because if m is not of the form x^2 + n*y^2 and m^(r-2) is not of the form x^2 + n*y^2, but m^r = a^2 + n*b^2, then m^(r+2) = (m*a)^2+n*(m*b)^2, m^(r+4) = (m^2*a)^2+n*(m^2*b)^2, etc. are also of the form x^2 + n*y^2. Then m^(3*r-6) = (m^(r-2))^3 = (m^(r-3)*a)^2 + n*(m^(r-3)*b)^2 is of the form x^2 + n*y^2 and m^(r-2) is not of the form x^2 + n*y^2.
%C A232527 All squarefree convenient numbers (A000926) congruent to {1, 2, 3, 5, 6} mod 8 are members of this sequence.
%C A232527 It appears that for a given value of n, if there is an m such that m^3 is of the form x^2 + n*y^2 and m is not of the form x^2 + n*y^2, then there exists some m < n that satisfies this condition.
%C A232527 Is this sequence finite?
%C A232527 Is 66045 the largest term of this sequence?
%H A232527 V. Raman, <a href="/A232527/b232527.txt">Table of n, a(n) for n = 1..172</a>
%e A232527 n = 11 is not a member of this sequence because for m = 23, 23 is not of form x^2 + 11*y^2, but 23^3 = 12167 = 54^2 + 11*29^2.
%o A232527 (PARI) for(n=1,100000,flag=0;for(m=1,n,a=0;b=0;for(x=0,ceil(sqrt(m/n)),if(issquare(m-n*x^2),a=1; break));if(a==0,for(y=0,ceil(sqrt(m^3/n)),if(issquare(m^3-n*y^2),b=1; break)));if(a==0&&b==1,flag=1));if(flag==0,print1(n", ")))
%Y A232527 Cf. A000926.
%K A232527 nonn
%O A232527 1,2
%A A232527 _V. Raman_, Nov 25 2013