OFFSET
1,1
LINKS
Vincenzo Librandi, Chai Wah Wu, and Charles R Greathouse IV, Table of n, a(n) for n = 1..1000 (1..57 from Librandi, 58..246 from Wu)
H. E. Dudeney, Amusements in Mathematics, Nelson, London, 1917, Problem 135.
EXAMPLE
312^2 = 97344 = 14^3 + 15^3 + ... + 25^3.
MATHEMATICA
nn = 500; t = Table[n^3, {n, 2, nn}]; t2 = Table[Total[Take[t, {i, j}]], {i, nn - 1}, {j, i + 3, nn - 1}]; t3 = Select[Union[Flatten[t2]], # <= nn^3 &]; Select[t3, IntegerQ[#^(1/2)] &]^(1/2) (* T. D. Noe, Feb 25 2014 *)
nn=1000; With[{c=Range[2, nn]^3}, Sort[Select[Sqrt[#]&/@ Flatten[ Table[ Total/@ Partition[c, n, 1], {n, 4, nn}]], IntegerQ]]] (* Harvey P. Dale, Apr 28 2014 *)
PROG
(PARI) list(lim)=my(v=List(), L2=(lim\=1)^2, s, t); for(n=25, sqrtnint(lim^2\3, 3)+1, s=3*n^3 - 9*n^2 + 15*n - 9; forstep(k=n-3, 2, -1, s+=k^3; if(s>L2, break); if(issquare(s, &t), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Nov 13 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 25 2014
STATUS
approved