A235602 a(n) = n/wt(n) if wt(n) divides n, otherwise a(n) = n, where wt(n) is the binary weight of n (A000120).

1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 6, 13, 14, 15, 16, 17, 9, 19, 10, 7, 22, 23, 12, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17, 35, 18, 37, 38, 39, 20, 41, 14, 43, 44, 45, 46, 47, 24, 49, 50, 51, 52, 53, 54, 11, 56, 57, 58, 59, 15, 61, 62, 63, 64, 65, 33, 67, 34, 23, 70, 71, 36, 73, 74, 75, 76, 77, 78, 79, 40, 27, 82

Offset: 1

Author

N. J. A. Sloane, Jan 18 2014

Keywords

• nonn
• base
• easy

Links

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

Crossrefs

Cf. A000079, A000120, A049445, A065878, A235600, A235601.

Programs

Mathematica

bw[n_]:=Module[{w=DigitCount[n,2,1]},If[Divisible[n,w],n/w,n]]; Array[ bw,90] (* Harvey P. Dale, Nov 06 2016 *)

PARI

a(n) = my(s=hammingweight(n)); if (n % s, n, n/s); \\ Michel Marcus, Jul 15 2021

Formula

From Amiram Eldar, Aug 04 2025: (Start)

a(n) = n if and only if n is in A065878 or A000079.

a(n) < n if and only if n is in A049445 but not in A000079. (End)