A364006 Wythoff-Niven numbers: numbers that are divisible by the number of 1's in their Wythoff representation.

1, 3, 4, 6, 7, 8, 10, 12, 15, 18, 20, 21, 24, 26, 28, 32, 35, 39, 40, 42, 45, 47, 51, 52, 54, 55, 56, 60, 68, 72, 76, 80, 84, 86, 88, 90, 91, 98, 100, 102, 105, 117, 120, 123, 125, 135, 136, 138, 141, 143, 144, 156, 164, 168, 172, 174, 176, 178, 180, 188, 192

Offset

1,2

Comments

Numbers k such that A135818(k) | k.

Includes all the positive even-indexed Fibonacci numbers (A001906), since the Wythoff representation of Fibonacci(2*n), for n >= 1, is 1 followed by n-1 0's.

Links

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

Mathematica

wnQ[n_] := (s = Total[w[n]]) > 0 && Divisible[n, s] (* using the function w[n] from A364005 *)

Crossrefs

Cf. A135818, A189921.

Subsequences: A364007, A364008, A364009.

Similar sequences: A005349, A049445, A064150, A064438, A064481, A118363, A328208, A328212, A331085, A333426, A342726, A334308, A331728, A342426, A344341, A351714, A351719, A352089, A352107, A352320, A352508.

Sequence in context: A087758 A227019 A105454 * A283482 A283471 A127260

Adjacent sequences: A364003 A364004 A364005 * A364007 A364008 A364009

Keyword

nonn,base

Author

Amiram Eldar, Jul 01 2023

Status

approved