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

1,1

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.

Links

Table of n, a(n) for n=1..21.

Example

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

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 *)

Crossrefs

Subsequence of A338514 and A338515.

Cf. A000120, A093653, A093705.

Similar sequences: A141769, A330933, A334372, A338454.

Sequence in context: A068746 A343078 A345010 * A091443 A114888 A347114

Adjacent sequences: A338513 A338514 A338515 * A338517 A338518 A338519

Keyword

nonn,base

Author

Amiram Eldar, Oct 31 2020

Status

approved