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 A129316 #16 Oct 26 2019 09:57:25
%S A129316 5,8,15,77,125,160,252,496,714,948,980,1045,1053,1260,1330,1378,1404,
%T A129316 1430,1508,1520,1610,1750,1862,1890,2170,2491,2680,2821,3094,3100,
%U A129316 3248,3400,3591,3610,3652,3808,4185,4191,4384,4452,4500,4598,4906,5120,5145
%N A129316 Positive integers k such that sopfr(k) divides sopfr(k+1), where sopfr(k) is the sum of the prime factors of k, counting multiplicity.
%C A129316 A generalization of Ruth-Aaron pairs (A006145).
%H A129316 Amiram Eldar, <a href="/A129316/b129316.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%F A129316 sopfr(k+1) mod sopfr(k) = 0.
%e A129316 a(6)=160 since sopfr(160)=sopfr(2^5*5)=10+5=15 and sopfr(161)=sopfr(7*23)=30.
%t A129316 sopf[n_]:=Total[Flatten[Table[#[[1]],{#[[2]]}]&/@FactorInteger[n]]]; Rest[ Flatten[Position[Partition[Table[sopf[n],{n,5200}],2,1],_?(Divisible[#[[2]],#[[1]]]&),{1},Heads->False]]] (* _Harvey P. Dale_, Jul 18 2013 *)
%Y A129316 Cf. A001414, A006145, A039752, A129317, A129318, A129319.
%K A129316 easy,nonn
%O A129316 1,1
%A A129316 _Walter Kehowski_, Apr 09 2007