OFFSET
1,16
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
FORMULA
a(n) = valuation(n,4).
G.f.: Sum_{k>=1} x^(4^k)/(1 - x^(4^k)). - Ilya Gutkovskiy, Jan 28 2017
Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/3. - Amiram Eldar, Jan 17 2022
EXAMPLE
Since 4^2 divides 32 and 4^3 does not, we have a(32) = 2. Likewise, since no positive power of 4 divides 9, a(9) = 0.
MATHEMATICA
IntegerExponent[Range@ 105, 4] (* Michael De Vlieger, Nov 18 2017 *)
PROG
(PARI) A235127(n) = valuation(n, 4); \\ Antti Karttunen, Nov 18 2017
(Sage)
n=100 #change n for more terms
[valuation(i, 4) for i in [1..n]]
(Python)
def A235127(n): return (~n&n-1).bit_length()>>1 # Chai Wah Wu, Jul 08 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Tom Edgar, Jan 03 2014
EXTENSIONS
More terms from Antti Karttunen, Nov 18 2017
STATUS
approved