A338516 - OEIS

%I #6 May 28 2023 15:35:49

%S 1377595575,4275143301,13616091683,13640596128,15016388244,

%T 15176619135,21361749754,23605084359,24794290167,28025464183,

%U 29639590888,30739547718,33924433023,35259630279,38008366692,38670247670,38681191672,40210059079,40507412213,49759198333,52555068607

%N Starts of runs of 4 consecutive numbers that are divisible by the total binary weight of their divisors (A093653).

%C 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 1377595575 is a term since the 4 consecutive numbers from 1377595575 to 1377595578 are all terms of A093705.

%t 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 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 Subsequence of A338514 and A338515.

%Y Cf. A000120, A093653, A093705.

%Y Similar sequences: A141769, A330933, A334372, A338454.

%K nonn,base

%O 1,1

%A _Amiram Eldar_, Oct 31 2020