A078130 Numbers having exactly one representation as sum of cubes > 1.

8, 16, 24, 27, 32, 35, 40, 43, 48, 51, 54, 56, 59, 62, 67, 70, 75, 78, 81, 83, 86, 89, 94, 97, 102, 105, 108, 110, 113, 116, 121, 124, 125, 129, 132, 133, 135, 137, 140, 141, 143, 148, 149, 151, 156, 157, 159, 162, 164, 165, 167, 170, 173, 175, 178, 181, 183, 186, 191, 194, 202, 210, 218

Offset: 1

Author

Reinhard Zumkeller, Nov 19 2002

Keywords

• nonn
• fini
• full

Comments

A078128(a(n))=1.

Conjecture: the sequence is finite; is a(63)=218 the last entry?

Yes. An argument similar to that in A078136 can be made, based on the identity m = 8*k = k*2^3 = 4^3 + (k-8)*2^3 which enables trading 4^3 for 8 repeats of 2^3. Then, the remaining residue classes m = 8*k+r for r=1..7 can be handled by known representations for m = 145, 226, 91, 172, 189, 118, and 199, respectively. - Sean A. Irvine, Jun 17 2025

Examples

			72 is not a term, as 72 = 8+8+8+8+8+8+8+8+8 = 8+64.
		

Links

• Eric Weisstein's World of Mathematics, Cubic Number.
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A000578, A078131, A078129, A078136.

Extensions

More terms from Sean A. Irvine, Jun 17 2025