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A126200
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Numbers n such that n^2 is a sum of consecutive cubes larger than 1.
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14
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8, 27, 64, 125, 204, 216, 312, 315, 323, 343, 504, 512, 588, 720, 729, 1000, 1331, 1728, 2079, 2170, 2197, 2744, 2940, 3375, 4096, 4472, 4913, 4914, 5187, 5832, 5880, 5984, 6630, 6859, 7497, 8000, 8721, 8778, 9261, 9360, 10296, 10648, 10695, 11024, 12167, 13104
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OFFSET
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1,1
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COMMENTS
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Note that all triangular numbers A000217(i) have squares A000217(i)^2=A000537(i), which are sums of consecutive cubes starting with 1. But such decompositions are not counted here. - R. J. Mathar, Nov 02 2007
Also, the positive integers n such that n^2 is the difference of squares of two positive triangular numbers. - Max Alekseyev, Jul 27 2014
Included all cubes > 1.
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LINKS
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EXAMPLE
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204^2=23^3+24^3+25^3, 312^2=14^3+15^3+...24^3+25^3;
n^2=sum[i^3, (i=i1...i2)]; {n, i1=initial index of cube, i2=final index of cube}: {8, 4, 4}, {27, 9, 9}, {64, 16, 16}, {125, 25, 25}, {204, 23, 25}, {216, 36, 36}, {312, 14, 25}, {315, 25, 29}, {323, 9, 25}, {343, 49, 49}, {504, 28, 35}, {512, 64, 64}, {588, 14, 34}, {720, 25, 39}, {729, 81, 81}, {1000, 100, 100}, {1331, 121, 121}, {1728, 144, 144}, {2079, 33, 65}, {2170, 96, 100}, {2197, 169, 169}, {2744, 196, 196}.
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PROG
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(PARI) mc=335241; cb=vector(mc); for(i=2, mc, cb[i]=i^3); v=vector(1000); mx=194104539^2; n=0; for(i=2, mc, s=0; for(j=i, mc, s=s+cb[j]; if(s>mx, next(2)); if(issquare(s, &sr), n++; v[n]=sr))); v=vecsort(v); for(i=1, 1000, write("b126200.txt", i " " v[i])) /* Donovan Johnson, Feb 02 2013 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Many terms were missing - thanks to Donovan Johnson for catching this. (Feb 02 2013)
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STATUS
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approved
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