A180490 Numbers k such that (A000120(k))^2 divides k.

1, 2, 4, 8, 12, 16, 20, 24, 32, 36, 40, 48, 64, 68, 72, 80, 81, 96, 128, 132, 136, 144, 160, 162, 192, 240, 252, 256, 260, 261, 264, 272, 288, 320, 324, 368, 384, 425, 432, 464, 480, 504, 512, 516, 520, 522, 528, 544, 576, 624, 625, 637, 640, 648, 675, 688, 720

Offset: 1

Author

Ctibor O. Zizka, Sep 08 2010

Keywords

• easy
• nonn
• base

Comments

This is a subsequence of A049445.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A049445.

Programs

Mathematica

fQ[n_] := Divisible[ n, DigitCount[n, 2, 1]^2]; Select[ Range@ 735, fQ] (* Robert G. Wilson v, Sep 10 2010 *)

PARI

isok(k) = !(k % hammingweight(k)^2); \\ Amiram Eldar, Jan 10 2025

Python

def ok(n): return n and n%n.bit_count()**2 == 0
print([k for k in range(721) if ok(k)]) # Michael S. Branicky, Jan 10 2025

Formula

{k: (A000120(k))^2 | k}.

Extensions

a(43) onwards from Robert G. Wilson v, Sep 10 2010