A048931 Numbers that are the sum of 6 positive cubes in exactly 3 ways.

221, 254, 369, 411, 443, 469, 495, 502, 576, 595, 600, 648, 658, 684, 704, 711, 720, 739, 746, 753, 760, 765, 767, 772, 774, 779, 786, 793, 811, 818, 828, 835, 844, 854, 863, 866, 874, 880, 884, 886, 892, 893, 899, 905, 910, 919, 928, 929, 935, 936, 937

Offset

1,1

Comments

It appears that this sequence has 1141 terms, the last of which is 26132. - Donovan Johnson, Jan 09 2013

Links

Donovan Johnson, Table of n, a(n) for n = 1..1141 (terms < 10^7)

Eric Weisstein's World of Mathematics, Cubic Number.

Example

221 is in the sequence since 221 = 216+1+1+1+1+1 = 125+64+8+8+8+8 = 64+64+64+27+1+1

Mathematica

Reap[For[n = 1, n <= 1000, n++, pr = Select[ PowersRepresentations[n, 6, 3], Times @@ # != 0 &]; If[pr != {} && Length[pr] == 3, Print[n, pr]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Jul 31 2013 *)

Prog

(PARI) mx=10^6; ct=vector(mx); cb=vector(99); for(i=1, 99, cb[i]=i^3); for(i1=1, 99, s1=cb[i1]; for(i2=i1, 99, s2=s1+cb[i2]; if(s2+4*cb[i2]>mx, next(2)); for(i3=i2, 99, s3=s2+cb[i3]; if(s3+3*cb[i3]>mx, next(2)); for(i4=i3, 99, s4=s3+cb[i4]; if(s4+2*cb[i4]>mx, next(2)); for(i5=i4, 99, s5=s4+cb[i5]; if(s5+cb[i5]>mx, next(2)); for(i6=i5, 99, s6=s5+cb[i6]; if(s6>mx, next(2)); ct[s6]++)))))); n=0; for(i=6, mx, if(ct[i]==3, n++; write("b048931.txt", n " " i))) /* Donovan Johnson, Jan 09 2013 */

Crossrefs

Cf. A003329, A048929, A048930, A343705, A345512, A345766, A345775, A345815.

Sequence in context: A159565 A330281 A345512 * A052478 A257752 A147284

Adjacent sequences: A048928 A048929 A048930 * A048932 A048933 A048934

Keyword

nonn

Author

Eric W. Weisstein

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Oct 02 2000

Status

approved