A074202 Numbers k such that the number of 1's in the binary expansion of k divides 2^k-1.

1, 2, 4, 8, 14, 16, 22, 26, 28, 32, 38, 42, 44, 50, 52, 56, 64, 70, 74, 76, 82, 84, 88, 98, 100, 104, 112, 124, 128, 134, 138, 140, 146, 148, 152, 162, 164, 168, 176, 188, 194, 196, 200, 208, 220, 224, 236, 244, 248, 256, 262, 266, 268, 274, 276, 280, 290, 292

Offset: 1

Author

Benoit Cloitre, Sep 17 2002

Keywords

• base
• easy
• nonn

Comments

Odd terms (1, 351, 375, ...) are in A074203.

Links

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

Crossrefs

Cf. A000120, A000225, A074203, A074293.

Different from A128309.

Programs

Mathematica

Select[Range[300], (d = DigitCount[#, 2, 1]) == 1 || PowerMod[2, #, d] == 1 &] (* Amiram Eldar, Jul 30 2020 *)

PARI

isok(n) = !((2^n-1) % hammingweight(n)); \\ Michel Marcus, Nov 29 2013

Python

from itertools import count, islice
def A074202_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:not ((1<A074202_list = list(islice(A074202_gen(),20)) # Chai Wah Wu, Mar 09 2023

Extensions

Edited by N. J. A. Sloane, May 10 2007