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 A093035 #11 May 19 2020 19:12:55
%S A093035 0,0,1,4,1,17,1,20,8,20,1,103,1,20,27,54,1,109,1,112,27,20,1,315,8,20,
%T A093035 27,112,1,315,1,112,27,20,27,481,1,20,27,324,1,321,1,112,125,20,1,695,
%U A093035 8,112,27,112,1,321,27,324,27,20,1,1285,1,20
%N A093035 Number of triples (d1,d2,d3) where each element is a divisor of n and d1 + d2 + d3 <= n.
%C A093035 It appears that a(n) depends on both parity of n and its prime signature. For instance a(odd prime)=1, a(even semiprime)=20, a(odd semiprime)=27, a(odd prime cube)=27, a(odd prime fourth power)=64. Maybe it is possible to find a formula for a(n). Similar sequences with pairs, quadruples, ... instead of triples can be envisioned. - _Michel Marcus_, Aug 21 2013
%C A093035 There's more to the story above. It seems that a(A233819(n)) gives the largest possible value per prime signature. Some prime signatures may have more than two possible values for a(n). - _David A. Corneth_, May 19 2020
%H A093035 Antti Karttunen, <a href="/A093035/b093035.txt">Table of n, a(n) for n = 1..16384</a>
%H A093035 Antti Karttunen, <a href="/A093035/a093035.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%e A093035 a(9) = 8 because the divisors of 9 are {1,3,9} making the valid triples (1,1,1), (1,1,3), (1,3,1), (1,3,3), (3,1,1), (3,1,3), (3,3,1), (3,3,3).
%o A093035 (PARI) a(n) = {nb = 0; d = divisors(n); for (i = 1, #d, for (j = 1, #d, for (k = 1, #d, if (d[i]+d[j]+d[k] <= n, nb++);););); nb;} \\ _Michel Marcus_, Aug 21 2013
%Y A093035 Cf. A233819.
%K A093035 easy,nonn
%O A093035 1,4
%A A093035 Jonathan A. Cohen (cohenj02(AT)tartarus.uwa.edu.au), May 08 2004