OFFSET
0,4
LINKS
Kenny Lau, Table of n, a(n) for n = 0..3323
FORMULA
From Ridouane Oudra, Sep 03 2019: (Start)
a(n) = Sum_{i=1..n} 2^(n-i)*v_2(i), where v_2(i) = A007814(i).
More generally, the p-adic valuation of A052129 for any prime p is given by
v_p(A052129(n)) = Sum_{i=1..n} 2^(n-i)*v_p(i), where v_p(i) is the exponent of the highest power of p dividing i. (End)
MAPLE
with(padic): seq(add(2^(n-i)*ordp(i, 2), i=1..n), n=0..60); # Ridouane Oudra, Sep 03 2019
MATHEMATICA
Map[IntegerExponent[#, 2] &, Nest[Append[#, Length[#]*#[[-1]]^2] &, {1}, 31]] (* or, per first formula, more efficiently, *)
Array[Sum[2^(# - i)*IntegerExponent[i, 2], {i, #}] &, 32, 0] (* Michael De Vlieger, Sep 29 2019 *)
PROG
(PARI)
A052129(n) = if( n<1, n==0, prod(k=0, n-1, (n - k)^2^k));
a(n) = valuation(A052129(n), 2);
(PARI) a(n) = fromdigits(vector(n, i, valuation(i, 2)), 2); \\ Kevin Ryde, Oct 08 2021
(Python)
n=4000; val=[0]*(n+1); exp=2
while exp <= n:
for j in range(exp, n+1, exp): val[j] += 1
exp *= 2
res = 0; i = 0
while len(str(res)) <= 1000: print(i, res); i += 1; res = res * 2 + val[i]
# Kenny Lau, Jun 09 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt, Feb 27 2014
EXTENSIONS
Incorrect comment removed by Michel Marcus, Oct 06 2019
STATUS
approved