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 A335018 #7 Jun 20 2020 01:14:43 %S A335018 0,1,8,27,27,125,64,343,343,512,125,1331,729,1331,216,3375,3375,1331, %T A335018 4913,2744,343,6859,3375,12167,2197,12167,4913,512,12167,6859,29791, %U A335018 3375,17576,24389,29791,42875,8000,729,29791,19683,12167,59319,4913,42875,42875,103823,13824 %N A335018 Number of triples (d1,d2,d3) where each element is a divisor of m and d1 + d2 + d3 <= m where m is least odd integer of each prime signature. %C A335018 All terms are cubes. Proof: Let d_k be the k-th divisor of some odd m > 1 and t be the number of divisors of m. Then d_(t-1) is <= n/3 and so any sum of 3 divisors of at most d_(t-1) is at most n and so that sum is counted per A093035. A sum of 3 divisors of m where one of the divisors is d_t = m as more than m so not counted. This gives (t-1)^3 possible triples hence all terms are cubes. %F A335018 a(n) = A093035(A147516(n)). %F A335018 a(n) = A000005(A147516(n) - 1)^3. %e A335018 A147516(6) = 45 so a(6) = A093035(45) = (tau(45) - 1)^3. %Y A335018 Cf. A000005, A093035, A147516. %K A335018 nonn,easy %O A335018 1,3 %A A335018 _David A. Corneth_, May 19 2020