A122054 - OEIS

%I #24 Jul 12 2016 23:07:03

%S 1,2,17,1737,1025,92025,3375900,5472225,35964225,930860225,1000837225,

%T 4979585600,38515961025,88154795025,203947076025,88813460025,

%U 5684061441600,77806025000000,64745012358225

%N Least positive number with exactly n partitions into a square and a cube.

%C The sequence is not monotonic.

%C Equals 1 followed by A060835.

%F m=a^2+b^3, a,b>0.

%e a(0)=1 because there's no partition of 1 into a square and a cube;

%e a(1)=2 because 2 = 1^2 + 1^3, one partition;

%e a(2)=17 because 17 = 3^2 + 2^3 = 4^2 + 1^3, two partitions;

%e a(3)=1737 because 1737 = 3^2 + 12^3 = 35^2 + 8^3 = 39^2 + 6^3, three partitions, etc.

%e Table of partitions:

%e {m,{a_i,b_i}}

%e {1,{-}}

%e {2,{1,1}}

%e {17,{3,2},{4,1}}

%e {1737,{3,12},{35,8},{39,6}}

%e {1025,{5,10},{30,5},{31,4},{32,1}}

%e {92025,{30,45},{152,41},{213,36},{255,30},{303,6}}

%e {3375900,{30,150},{1430,110},{1551,99},{1794,54},{1830,30},{1837,11}}

%e {5472225,{143,176},{990,165},{1935,120},{2035,110},{2251,74},{2277,66},{2321,44}}

%e {35964225,{165,330},{3167,296},{4035,270},{4191,264},{5610,165},{5885,110},{5973,66},{5997,6}}

%e {930860225,{13315,910},{23139,734},{26817,596},{29560,385},{30271,244},{30335,220},{30460,145},{30465,140},{30510,5}}

%e {1000837225,{915,1000},{16921,894},{19665,850},{20960,825},{24735,730},{29465,510},{30221,444},{31608,121},{31635,40},{31636,9}}

%e {4979585600,{8160,1700},{24512,1636},{40392,1496},{48785,1375},{49640,1360},{64515,935},{65560,880},{66840,800},{69960,440},{70024,424},{70565,55}}

%e {38515961025,{20330,3365},{41507,3326},{73755,3210},{95084,3089},{115595,2930},{118431,2904},{132255,2760},{153953,2456},{176355,1950},{190305,1320},{195570,645},{196254,69}}

%Y Cf. A060835, A123388.

%K nonn,more

%O 0,2

%A _Zak Seidov_, Oct 15 2006

%E Corrected a(7), added a(8)-a(12) from _Lars Blomberg_, Feb 15 2016