A076749 - OEIS

A076749

Least number which is the sum of four nonnegative cubes (not necessarily distinct and including zero) in n ways.

%I #14 Aug 31 2013 19:33:42

%S 0,81,856,1584,4949,5859,13104,20755,34776,21896,46683,46872,81081,

%T 77896,151424,143640,116200,231336,216216,369152,420147,314496,373464,

%U 375193,483840,648648,353808,497952,995904,687960,975240,1199016,1120392,1081080,1434888

%N Least number which is the sum of four nonnegative cubes (not necessarily distinct and including zero) in n ways.

%H Donovan Johnson, <a href="/A076749/b076749.txt">Table of n, a(n) for n = 1..250</a>

%H G. Villemin's Almanach of Numbers, <a href="http://villemin.gerard.free.fr/Wwwgvmm/Addition/NoSoCu4f.htm#Presentation">Sum of Four cubes:Multiple Representations</a>

%e a(3) = 856 because the latter is the smallest number expressible as the sum of four cubes in 3 distinct ways, namely 856 = 0^3 + 1^3 + 7^3 + 8^3 = 1^3 + 1^3 + 5^3 + 9^3 = 4^3 + 4^3 + 6^3 + 8^3.

%o (PARI) mx=10^7; v=vector(mx+1); cb=vector(216); for(j=0, 215, cb[j+1]=j^3); for(j1=1, 136, for(j2=j1, 150, s2=cb[j1]+cb[j2]; for(j3=j2, 171, s3=s2+cb[j3]; if(s3+cb[j3]>mx, next(2)); for(j4=j3, 216, s4=s3+cb[j4]; if(s4>mx, next(2)); v[s4+1]++)))); for(n=1, 68, for(j=1, mx+1, if(v[j]==n, print(n " " j-1); next(2)))) /* _Donovan Johnson_, Apr 16 2013 */

%K nonn

%O 1,2

%A _Lekraj Beedassy_, Nov 12 2002

%E More terms from _Jon E. Schoenfield_, Jul 23 2006