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 A338516 #6 May 28 2023 15:35:49
%S A338516 1377595575,4275143301,13616091683,13640596128,15016388244,
%T A338516 15176619135,21361749754,23605084359,24794290167,28025464183,
%U A338516 29639590888,30739547718,33924433023,35259630279,38008366692,38670247670,38681191672,40210059079,40507412213,49759198333,52555068607
%N A338516 Starts of runs of 4 consecutive numbers that are divisible by the total binary weight of their divisors (A093653).
%C A338516 Can 5 consecutive numbers be divisible by the total binary weight of their divisors? If they exist, then they are larger than 10^11.
%e A338516 1377595575 is a term since the 4 consecutive numbers from 1377595575 to 1377595578 are all terms of A093705.
%t A338516 divQ[n_] := Divisible[n, DivisorSum[n, DigitCount[#, 2, 1] &]]; div = divQ /@ Range[4]; Reap[Do[If[And @@ div, Sow[k - 4]]; div = Join[Rest[div], {divQ[k]}], {k, 5, 5*10^9}]][[2, 1]]
%t A338516 SequencePosition[Table[If[Mod[n,Total[Flatten[IntegerDigits[#,2]&/@Divisors[n]]]]==0,1,0],{n,526*10^8}],{1,1,1,1}][[;;,1]] (* The program will take a long time to run. *) (* _Harvey P. Dale_, May 28 2023 *)
%Y A338516 Subsequence of A338514 and A338515.
%Y A338516 Cf. A000120, A093653, A093705.
%Y A338516 Similar sequences: A141769, A330933, A334372, A338454.
%K A338516 nonn,base
%O A338516 1,1
%A A338516 _Amiram Eldar_, Oct 31 2020