%I A156668
%S A156668 1,11,101,13361,1169341,1612186411,1624763543401,20188985439712961,
%T A156668 240020196429554642201,29891946989942513908518251,
%U A156668 3506790234728288196345900732301,5190947078637547438603476743093680561
%N A156668 Positive integers k such that k^2 = (m^5+n^5)/(m+n) for some co-prime 
               integers m,n.
%F A156668 Numerators of rational numbers (81*x^4+540*x^3-8370*x^2+33900*x-47975)/
               (9*x^2 - 150*x + 445)^2, where x ranges over abscissas of rational 
               points on the elliptic curve y^2 = x^3 - 85/3*x + 1550/27.
%e A156668 13361 belongs to this sequence since 13361^2 = (35^5 + 123^5) / (35 + 
               123) with gcd(35,123)=1.
%Y A156668 Cf. A156669, A156670
%Y A156668 Sequence in context: A020449 A089971 A082620 this_sequence A103992 A001387 
               A100580
%Y A156668 Adjacent sequences: A156665 A156666 A156667 this_sequence A156669 A156670 
               A156671
%K A156668 nonn
%O A156668 1,2
%A A156668 Max Alekseyev (maxale(AT)gmail.com), Feb 13 2009