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

1, 2, 17, 1737, 1025, 92025, 3375900, 5472225, 35964225, 930860225, 1000837225, 4979585600, 38515961025, 88154795025, 203947076025, 88813460025, 5684061441600, 77806025000000, 64745012358225

Offset

0,2

Comments

The sequence is not monotonic.

Equals 1 followed by A060835.

Links

Table of n, a(n) for n=0..18.

Formula

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

Example

a(0)=1 because there's no partition of 1 into a square and a cube;
a(1)=2 because 2 = 1^2 + 1^3, one partition;
a(2)=17 because 17 = 3^2 + 2^3 = 4^2 + 1^3, two partitions;
a(3)=1737 because 1737 = 3^2 + 12^3 = 35^2 + 8^3 = 39^2 + 6^3, three partitions, etc.
Table of partitions:
{m,{a_i,b_i}}
{1,{-}}
{2,{1,1}}
{17,{3,2},{4,1}}
{1737,{3,12},{35,8},{39,6}}
{1025,{5,10},{30,5},{31,4},{32,1}}
{92025,{30,45},{152,41},{213,36},{255,30},{303,6}}
{3375900,{30,150},{1430,110},{1551,99},{1794,54},{1830,30},{1837,11}}
{5472225,{143,176},{990,165},{1935,120},{2035,110},{2251,74},{2277,66},{2321,44}}
{35964225,{165,330},{3167,296},{4035,270},{4191,264},{5610,165},{5885,110},{5973,66},{5997,6}}
{930860225,{13315,910},{23139,734},{26817,596},{29560,385},{30271,244},{30335,220},{30460,145},{30465,140},{30510,5}}
{1000837225,{915,1000},{16921,894},{19665,850},{20960,825},{24735,730},{29465,510},{30221,444},{31608,121},{31635,40},{31636,9}}
{4979585600,{8160,1700},{24512,1636},{40392,1496},{48785,1375},{49640,1360},{64515,935},{65560,880},{66840,800},{69960,440},{70024,424},{70565,55}}
{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}}

Crossrefs

Cf. A060835, A123388.

Sequence in context: A058233 A062635 A060835 * A284706 A092415 A274053

Adjacent sequences: A122051 A122052 A122053 * A122055 A122056 A122057

Keyword

nonn,more

Author

Zak Seidov, Oct 15 2006

Extensions

Corrected a(7), added a(8)-a(12) from Lars Blomberg, Feb 15 2016

Status

approved