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

Author

Leroy Quet, Jun 03 2009

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A161150, A000265, A006519, A002378.

Programs

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 *)

PARI

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

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

Extensions

Extended by Ray Chandler, Jun 11 2009