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A160467 a(n) = 1 if n is odd; otherwise, a(n) = 2^(k-1) where 2^k is the largest power of 2 that divides n. 5
1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 16, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 32, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Fifth factor of the row sums A160466 of the Eta triangle A160464.

Contribution from Peter Luschny, May 31 2009: (Start)

Let odd(n) by the characteristic function of the odd numbers (A000035) and sigma(n) the number of 1's in binary expansion of n (A000120) then

a(n) = 2^(sigma(n-1) - sigma(n) + odd(n)).

Let B_{n} be the Bernoulli number. Then this sequence is also

a(n) = denominator(4*(4^n-1)*B_{2*n}/n). (End)

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

FORMULA

a(n) = A026741(n)/A000265(n). - Paul Curtz, Apr 18 2010

a(n) = 2^max(A007814(n) - 1, 0). - Max Alekseyev, Feb 09 2011

a((2*n-1)*2^p) = A011782(p), p >= 0 and n >= 1. - Johannes W. Meijer, Jan 25 2013

a(n) = (1 + A140670(n))/2. - Antti Karttunen, Nov 18 2017

MAPLE

nmax:=96: p:= floor(log[2](nmax)): for n from 1 to nmax do a(n):=1 end do: for q from 1 to p do for n from 1 to nmax do if n mod 2^q = 0 then a(n):= 2^(q-1) end if: end do: end do: seq(a(n), n=1..nmax);

Contribution from Peter Luschny, May 31 2009: (Start)

a := proc(n) local sigma; sigma := proc(n) local i; add(i, i=convert(n, base, 2)) end; 2^(sigma(n-1)-sigma(n)+`if`(type(n, odd), 1, 0)) end: seq(a(n), n=1..96);

a := proc(n) denom(4*(4^n-1)*bernoulli(2*n)/n) end: seq(a(n), n=1..96); (End)

PROG

(PARI) A160467(n) = 2^max(valuation(n, 2)-1, 0); \\ Antti Karttunen, Nov 18 2017, after Max Alekseyev's Feb 09 2011 formula.

CROSSREFS

Cf. A000265, A007814, A026741, A140670, A160464, A220466.

Sequence in context: A294616 A085384 A067856 * A122374 A261960 A010121

Adjacent sequences:  A160464 A160465 A160466 * A160468 A160469 A160470

KEYWORD

base,easy,nonn,mult

AUTHOR

Johannes W. Meijer, May 24 2009, Jun 28 2011

EXTENSIONS

Keyword mult added by Max Alekseyev, Feb 09 2011

Name changed by Antti Karttunen, Nov 18 2017

STATUS

approved

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Last modified November 16 22:43 EST 2018. Contains 317275 sequences. (Running on oeis4.)