A161151 a(n) = (largest odd divisor of (n+1))*(largest power of 2 dividing n).

1, 6, 1, 20, 3, 14, 1, 72, 5, 22, 3, 52, 7, 30, 1, 272, 9, 38, 5, 84, 11, 46, 3, 200, 13, 54, 7, 116, 15, 62, 1, 1056, 17, 70, 9, 148, 19, 78, 5, 328, 21, 86, 11, 180, 23, 94, 3, 784, 25, 102, 13, 212, 27, 110, 7, 456, 29, 118, 15, 244, 31, 126, 1, 4160, 33, 134, 17, 276, 35

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..16384

Formula

a(n)*A161150(n) = n*(n+1) = A002378(n).

a(n) = A000265(n+1)*A006519(n).

a(2^k*(2*n-1) - 1) = 2*n-1 and a(2^k*(2*n-1)) = 2^k*(1 + 2^k*(2*n-1)), n >= 1 and k >= 1. - Johannes W. Meijer, Oct 31 2012

1 <= a(n) <= n^2 + n; both bounds are sharp. - Charles R Greathouse IV, Oct 31 2012

a(2*n-1) = A000265(n) and a(2*n) = 2*A182241(n) - Johannes W. Meijer, Dec 24 2012

Maple

nmax:=69: for n from 1 to nmax do for k from 1 to floor(log[2](nmax)) do a(2^k*(2*n-1) - 1) := 2*n-1; a(2^k*(2*n-1)) := 2^k*(1 + 2^k*(2*n-1)) od: od: seq(a(n), n=1..nmax); # Johannes W. Meijer, Oct 31 2012

Mathematica

Array[SelectFirst[Reverse@ Divisors[# + 1], OddQ]*2^IntegerExponent[#, 2] &, 69] (* Michael De Vlieger, Nov 02 2017 *)

Prog

(PARI) a(n)=(n+1)>>valuation(n+1, 2)<<valuation(n, 2) \\ Charles R Greathouse IV, Oct 31 2012

Crossrefs

Cf. A161150, A000265, A006519, A002378.

Sequence in context: A200091 A180733 A334504 * A146383 A264313 A096130

Adjacent sequences: A161148 A161149 A161150 * A161152 A161153 A161154

Keyword

nonn,easy

Author

Leroy Quet, Jun 03 2009

Extensions

Extended by Ray Chandler, Jun 11 2009

Status

approved