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A082908 Largest value of gcd(2^n, binomial(n,j)) with j=0..n-1; maximal value of largest power of 2 dividing binomial(n,j) in the n-th row of Pascal's triangle. 1
1, 1, 2, 1, 4, 2, 4, 1, 8, 4, 8, 2, 8, 4, 8, 1, 16, 8, 16, 4, 16, 8, 16, 2, 16, 8, 16, 4, 16, 8, 16, 1, 32, 16, 32, 8, 32, 16, 32, 4, 32, 16, 32, 8, 32, 16, 32, 2, 32, 16, 32, 8, 32, 16, 32, 4, 32, 16, 32, 8, 32, 16, 32, 1, 64, 32, 64, 16, 64, 32, 64, 8, 64, 32, 64, 16, 64, 32, 64, 4, 64, 32 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..81.

FORMULA

a(n) = Max_{gcd(2^n, binomial(n, j)), j=0..n}.

a(n-1) = 2^floor(log_2(A000265(n))). - Brad Clardy, May 06 2013

EXAMPLE

n=10: 10th row = {1,10,45,120,210,252,210,120,45,10,1}, largest powers of 2 dividing entries: {1,2,1,8,2,4,2,8,1,2,1}; maximal 2^k-divisor is a(10)=8.

MATHEMATICA

Table[Max[Table[GCD[2^n, Binomial[n, j]], {j, 0, n}]], {n, 0, 128}]

PROG

(PARI) a(n)=n--; 2^(log(n>>valuation(n, 2)+.5)\log(2)) \\ Charles R Greathouse IV, May 06 2013

CROSSREFS

Cf. A000005, A007318, A000079, A082907, A000265.

Sequence in context: A153279 A278425 A309019 * A086449 A321088 A070556

Adjacent sequences:  A082905 A082906 A082907 * A082909 A082910 A082911

KEYWORD

nonn,tabl

AUTHOR

Labos Elemer, Apr 23 2003

STATUS

approved

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Last modified June 14 01:29 EDT 2021. Contains 345016 sequences. (Running on oeis4.)