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URL: https://oeis.org/A338516

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A338516
Starts of runs of 4 consecutive numbers that are divisible by the total binary weight of their divisors (A093653).
0
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.
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.
Similar sequences: A141769, A330933, A334372, A338454.
Sequence in context: A068746 A343078 A345010 * A091443 A114888 A347114
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Oct 31 2020
STATUS
approved