A092097 - OEIS

%I #12 Sep 24 2018 16:53:14

%S 2,5,8,22,47,103,234,493,1087,2282,4901,10427,21993,46389,97394,

%T 204567,427099,892587,1858338,3865692,8027140,16642918,34463760,

%U 71273199,147235636,303814862,626313383,1289883519,2654196000

%N Limit number of (m-n)-almost-primes in range [2^m..2^{m+1}-1].

%C Also number of odd numbers k for which floor(log_2(k)) - bigomega(k) = n, where bigomega is A001222. - _Franklin T. Adams-Watters_, Jun 20 2006

%C The value of m at which the number of (m-n)-almost-primes reaches its limit is floor(n/(log_2(3)-1))+n-1: 1,4,7,9,12,15,17,20,23,26,28; not A026356: 2,4,7,9,12,15,17,20,22,25,28 as originally conjectured. - _Franklin T. Adams-Watters_, Jun 20 2006

%F For n>0, a(n) = A052130(n+1)-A052130(n).

%e a(0) = 2: m-almost primes in [2^m..2^{m+1}-1] are 2^m and 3*2^{m-1}.

%e a(1) = 5; (m-1)-almost-primes in [2^m..2^{m-1}] are 5*2^{m-2}, 7*2^{m-2}, 9*2^{m-3}, 15*2^{m-3} and 27*2^{m-4}.

%Y Cf. A052130, A001222, A026356, A120033-A120043.

%K easy,nonn

%O 0,1

%A _Andrew S. Plewe_, Feb 19 2004

%E Edited and extended by _Franklin T. Adams-Watters_, Jun 20 2006