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A191871 a(n) = numerator(n^2 / 2^n). 6
0, 1, 1, 9, 1, 25, 9, 49, 1, 81, 25, 121, 9, 169, 49, 225, 1, 289, 81, 361, 25, 441, 121, 529, 9, 625, 169, 729, 49, 841, 225, 961, 1, 1089, 289, 1225, 81, 1369, 361, 1521, 25, 1681, 441, 1849, 121, 2025, 529, 2209, 9, 2401, 625, 2601, 169, 2809, 729, 3025 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
a(n+1) = largest odd divisor of A000290(n+1). - Jeremy Gardiner, Aug 25 2013
In binary, remove all trailing zeros, then square. - Ralf Stephan, Aug 26 2013
A fractal sequence. The odd-numbered elements give the odd squares A016754. If these elements are removed, the original sequence is recovered. - Jeremy Gardiner, Sep 14 2013
a(n+1) is the denominator of the population variance of the n-th row of Pascal's triangle. - Chai Wah Wu, Mar 25 2018
Multiplicative because A000265 is. - Andrew Howroyd, Jul 26 2018
LINKS
FORMULA
a(n) = A000265(n^2) = A000265(n)^2. - M. F. Hasler, Jun 19 2011
Recurrence: a(2n) = a(n), a(2n+1) = (2n+1)^2. - Ralf Stephan, Aug 26 2013
From Amiram Eldar, Nov 28 2022: (Start)
Multiplicative with a(2^e) = 1, and a(p^e) = p^(2*e) if p > 2.
Sum_{k=1..n} a(k) ~ (4/21) * n^3. (End)
Dirichlet g.f.: zeta(s-2)*(2^s-4)/(2^s-1). - Amiram Eldar, Jan 04 2023
MAPLE
[seq(numer(n^2/2^n), n=0..60)]; # Muniru A Asiru, Mar 31 2018
MATHEMATICA
a[n_] := Numerator[n^2/2^n]; Table[a[n], {n, 0, 200, 2}]
PROG
(PARI) a(n)=(n>>valuation(n, 2))^2 \\ Charles R Greathouse IV & M. F. Hasler, Jun 19 2011
(Python)
from __future__ import division
def A191871(n):
while not n % 2:
n //= 2
return n**2 # Chai Wah Wu, Mar 25 2018
(GAP) List([0..60], n->NumeratorRat(n^2/2^n)); # Muniru A Asiru, Mar 31 2018
CROSSREFS
Sequence in context: A205381 A237587 A328621 * A181318 A202006 A195278
KEYWORD
nonn,frac,easy,mult
AUTHOR
STATUS
approved

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Last modified May 29 22:36 EDT 2024. Contains 372954 sequences. (Running on oeis4.)