This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A078130 #25 Jun 18 2025 07:33:25 %S A078130 8,16,24,27,32,35,40,43,48,51,54,56,59,62,67,70,75,78,81,83,86,89,94, %T A078130 97,102,105,108,110,113,116,121,124,125,129,132,133,135,137,140,141, %U A078130 143,148,149,151,156,157,159,162,164,165,167,170,173,175,178,181,183,186,191,194,202,210,218 %N A078130 Numbers having exactly one representation as sum of cubes > 1. %C A078130 A078128(a(n))=1. %C A078130 Conjecture: the sequence is finite; is a(63)=218 the last entry? %C A078130 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 %H A078130 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubicNumber.html">Cubic Number</a>. %H A078130 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a> %e A078130 72 is not a term, as 72 = 8+8+8+8+8+8+8+8+8 = 8+64. %Y A078130 Cf. A000578, A078131, A078129, A078136. %K A078130 nonn,fini,full %O A078130 1,1 %A A078130 _Reinhard Zumkeller_, Nov 19 2002 %E A078130 More terms from _Sean A. Irvine_, Jun 17 2025