A338514 Numbers k such that k and k+1 are both divisible by the total binary weight of their divisors (A093653).

1, 2, 54, 2119, 11100, 13727, 14382, 15799, 16399, 20159, 20950, 33421, 34617, 36328, 36396, 39400, 42198, 42438, 42650, 46253, 46873, 50370, 55368, 56600, 58793, 67013, 67320, 69023, 72325, 76057, 86393, 90781, 92906, 93216, 105909, 132088, 134028, 134823, 140466

Offset

1,2

Comments

Numbers k such that k and k+1 are both in A093705, or, equivalently, k is divisible by A093653(k) and k+1 is divisible by A093653(k+1).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

1 is a term since 1 and 2 are both terms of A093705.

Mathematica

divQ[n_] := Divisible[n, DivisorSum[n, DigitCount[#, 2, 1] &]]; q1 = divQ[1]; Reap[Do[q2 = divQ[n]; If[q1 && q2, Sow[n - 1]]; q1 = q2, {n, 2, 10^5}]][[2, 1]]
SequencePosition[Table[If[Divisible[n, Total[DigitCount[Divisors[n], 2, 1]]], 1, 0], {n, 150000}], {1, 1}][[All, 1]] (* Harvey P. Dale, Jun 14 2022 *)

Crossrefs

Cf. A000120, A093653, A093705.

Similar sequences: A330927, A330931, A334345, A338452.

Sequence in context: A305693 A357421 A071798 * A123686 A122418 A069788

Adjacent sequences: A338511 A338512 A338513 * A338515 A338516 A338517

Keyword

nonn,base

Author

Amiram Eldar, Oct 31 2020

Status

approved