A161151 - OEIS

%I #20 Nov 02 2017 23:05:51

%S 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,

%T 7,116,15,62,1,1056,17,70,9,148,19,78,5,328,21,86,11,180,23,94,3,784,

%U 25,102,13,212,27,110,7,456,29,118,15,244,31,126,1,4160,33,134,17,276,35

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

%H Michael De Vlieger, <a href="/A161151/b161151.txt">Table of n, a(n) for n = 1..16384</a>

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

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

%F 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

%F 1 <= a(n) <= n^2 + n; both bounds are sharp. - _Charles R Greathouse IV_, Oct 31 2012

%F a(2*n-1) = A000265(n) and a(2*n) = 2*A182241(n) - _Johannes W. Meijer_, Dec 24 2012

%p 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

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

%o (PARI) a(n)=(n+1)>>valuation(n+1,2)<<valuation(n,2) \\ _Charles R Greathouse IV_, Oct 31 2012

%Y Cf. A161150, A000265, A006519, A002378.

%K nonn,easy

%O 1,2

%A _Leroy Quet_, Jun 03 2009

%E Extended by _Ray Chandler_, Jun 11 2009