A338516 Starts of runs of 4 consecutive numbers that are divisible by the total binary weight of their divisors (A093653).

1377595575, 4275143301, 13616091683, 13640596128, 15016388244, 15176619135, 21361749754, 23605084359, 24794290167, 28025464183, 29639590888, 30739547718, 33924433023, 35259630279, 38008366692, 38670247670, 38681191672, 40210059079, 40507412213, 49759198333, 52555068607

Offset: 1

Author

Amiram Eldar, Oct 31 2020

Keywords

• nonn
• base

Comments

Can 5 consecutive numbers be divisible by the total binary weight of their divisors? If they exist, then they are larger than 10^11.

Examples

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

Crossrefs

Subsequence of A338514 and A338515.

Cf. A000120, A093653, A093705.

Similar sequences: A141769, A330933, A334372, A338454.

Programs

Mathematica

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]]
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 *)