cp's OEIS Frontend

A122054 Least positive number with exactly n partitions into a square and a cube.

%I A122054 #24 Jul 12 2016 23:07:03
%S A122054 1,2,17,1737,1025,92025,3375900,5472225,35964225,930860225,1000837225,
%T A122054 4979585600,38515961025,88154795025,203947076025,88813460025,
%U A122054 5684061441600,77806025000000,64745012358225
%N A122054 Least positive number with exactly n partitions into a square and a cube.
%C A122054 The sequence is not monotonic.
%C A122054 Equals 1 followed by A060835.
%F A122054 m=a^2+b^3, a,b>0.
%e A122054 a(0)=1 because there's no partition of 1 into a square and a cube;
%e A122054 a(1)=2 because 2 = 1^2 + 1^3, one partition;
%e A122054 a(2)=17 because 17 = 3^2 + 2^3 = 4^2 + 1^3, two partitions;
%e A122054 a(3)=1737 because 1737 = 3^2 + 12^3 = 35^2 + 8^3 = 39^2 + 6^3, three partitions, etc.
%e A122054 Table of partitions:
%e A122054 {m,{a_i,b_i}}
%e A122054 {1,{-}}
%e A122054 {2,{1,1}}
%e A122054 {17,{3,2},{4,1}}
%e A122054 {1737,{3,12},{35,8},{39,6}}
%e A122054 {1025,{5,10},{30,5},{31,4},{32,1}}
%e A122054 {92025,{30,45},{152,41},{213,36},{255,30},{303,6}}
%e A122054 {3375900,{30,150},{1430,110},{1551,99},{1794,54},{1830,30},{1837,11}}
%e A122054 {5472225,{143,176},{990,165},{1935,120},{2035,110},{2251,74},{2277,66},{2321,44}}
%e A122054 {35964225,{165,330},{3167,296},{4035,270},{4191,264},{5610,165},{5885,110},{5973,66},{5997,6}}
%e A122054 {930860225,{13315,910},{23139,734},{26817,596},{29560,385},{30271,244},{30335,220},{30460,145},{30465,140},{30510,5}}
%e A122054 {1000837225,{915,1000},{16921,894},{19665,850},{20960,825},{24735,730},{29465,510},{30221,444},{31608,121},{31635,40},{31636,9}}
%e A122054 {4979585600,{8160,1700},{24512,1636},{40392,1496},{48785,1375},{49640,1360},{64515,935},{65560,880},{66840,800},{69960,440},{70024,424},{70565,55}}
%e A122054 {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 A122054 Cf. A060835, A123388.
%K A122054 nonn,more
%O A122054 0,2
%A A122054 _Zak Seidov_, Oct 15 2006
%E A122054 Corrected a(7), added a(8)-a(12) from _Lars Blomberg_, Feb 15 2016