A192085 Number of ones in the binary expansion of n^3.

0, 1, 1, 4, 1, 6, 4, 6, 1, 6, 6, 6, 4, 5, 6, 8, 1, 6, 6, 8, 6, 6, 6, 9, 4, 7, 5, 8, 6, 9, 8, 10, 1, 6, 6, 11, 6, 10, 8, 12, 6, 8, 6, 9, 6, 11, 9, 10, 4, 9, 7, 7, 5, 8, 8, 10, 6, 10, 9, 7, 8, 11, 10, 12, 1, 6, 6, 11, 6, 9, 11, 11, 6, 13, 10, 14, 8, 13, 12, 13

Offset: 0

Author

Carl R. White, Jun 23 2011

Keywords

• nonn
• base
• easy

Comments

The binary weight of n^3.

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000120, A000578, A007088, A159918.

Programs

Magma

[&+Intseq(n^3,2): n in [0..79]];  // Bruno Berselli, Jun 24 2011

Maple

A192085 := proc(n) return add(b,b=convert(n^3,base,2)): end: seq(A192085(n),n=0..100); # Nathaniel Johnston, Jun 23 2011

PARI

a(n)=hammingweight(n^3) \\ Charles R Greathouse IV, Sep 27 2016

Python

def A192085(n):
    return bin(n**3).count('1') # Chai Wah Wu, Sep 03 2014

Formula

a(n) = A000120(A000578(n)).

a(n) = [x^(n^3)] (1/(1 - x))*Sum_{k>=0} x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Mar 27 2018