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A238462 2-adic valuation of A052129. 4
0, 0, 1, 2, 6, 12, 25, 50, 103, 206, 413, 826, 1654, 3308, 6617, 13234, 26472, 52944, 105889, 211778, 423558, 847116, 1694233, 3388466, 6776935, 13553870, 27107741, 54215482, 108430966, 216861932, 433723865, 867447730 (list; graph; refs; listen; history; text; internal format)
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);

(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

Sequence in context: A045925 A128020 A140659 * A099495 A232164 A214663

Adjacent sequences:  A238459 A238460 A238461 * A238463 A238464 A238465

KEYWORD

nonn,changed

AUTHOR

Joerg Arndt, Feb 27 2014

EXTENSIONS

Incorrect comment removed by Michel Marcus, Oct 06 2019

STATUS

approved

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Last modified October 20 19:57 EDT 2019. Contains 328269 sequences. (Running on oeis4.)