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Number of ones in the binary expansion of n^3.
8

%I #21 Sep 08 2022 08:45:57

%S 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,

%T 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,

%U 12,1,6,6,11,6,9,11,11,6,13,10,14,8,13,12,13

%N Number of ones in the binary expansion of n^3.

%C The binary weight of n^3.

%H Nathaniel Johnston, <a href="/A192085/b192085.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

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

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

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

%o (Magma) [&+Intseq(n^3,2): n in [0..79]]; // _Bruno Berselli_, Jun 24 2011

%o (Python)

%o def A192085(n):

%o ....return bin(n**3).count('1') # _Chai Wah Wu_, Sep 03 2014

%o (PARI) a(n)=hammingweight(n^3) \\ _Charles R Greathouse IV_, Sep 27 2016

%Y Cf. A000120, A000578, A007088, A159918.

%K nonn,base,easy

%O 0,4

%A _Carl R. White_, Jun 23 2011