A308267 Numbers k such that k divides A048678(k).

1, 2, 4, 7, 8, 14, 16, 28, 31, 32, 56, 62, 64, 83, 112, 124, 127, 128, 166, 224, 248, 254, 256, 332, 397, 448, 496, 508, 511, 512, 664, 794, 891, 896, 992, 1016, 1022, 1024, 1163, 1328, 1588, 1782, 1792, 1984, 2032, 2044, 2047, 2048, 2326, 2656, 3176, 3441, 3564, 3584, 3968

Offset: 1

Author

Dan Dart, May 17 2019

Keywords

• nonn
• base

Comments

Apparently includes all powers of 2.

All numbers 2^(2k+1)-1 are in this sequence, and if n is in this sequence then so is 2n. - Charlie Neder, May 17 2019

Examples

			The first few terms of A048678 are 1,2,5,4,9,10,21,8. 2 is a multiple of 2, 5 isn't a multiple of 3, 4 is a multiple of 4, 9 isn't a multiple of 5, 10 isn't a multiple of 6, 21 is a multiple of 7, etc.
		

Crossrefs

Cf. A048678, A083420 (subsequence).

Programs

Haskell

bintodec :: [Integer] -> Integerbintodec = sum . zipWith (*) (iterate (*2) 1) . reverse
decomp :: (Integer, [Integer]) -> (Integer, [Integer])decomp (x, ys) = if even x then (x `div` 2, 0:ys) else (x - 1, 1:ys)
zeck :: Integer -> Integerzeck n = bintodec (1 : snd (last . takeWhile (\(x, _) -> x > 0) $ iterate decomp (n, [])))
output :: [Integer]output = filter (\x -> 0 == zeck x `mod` x) [1..100]
main :: IO ()main = print output

Mathematica

Select[Range[4000], Divisible[FromDigits[Flatten[IntegerDigits[#, 2] /. {1 -> {0, 1}}], 2], #] &] (* Amiram Eldar, Jul 08 2019 after Robert G. Wilson v at A048678 *)