

A126200


Numbers n such that n^2 is a sum of consecutive cubes larger than 1.


13



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

1,1


COMMENTS

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.


LINKS

Donovan Johnson, Table of n, a(n) for n = 1..1000


EXAMPLE

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}.


PROG

(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 */


CROSSREFS

Cf. A126203.
Sequence in context: A062686 A093322 A017670 * A213491 A276919 A076989
Adjacent sequences: A126197 A126198 A126199 * A126201 A126202 A126203


KEYWORD

nonn


AUTHOR

Zak Seidov, Mar 11 2007


EXTENSIONS

Better definition from Dean Hickerson, Dec 02 2007
Many terms were missing  thanks to Donovan Johnson for catching this. (Feb 02 2013)


STATUS

approved



