cp's OEIS Frontend

A092097 Limit number of (m-n)-almost-primes in range [2^m..2^{m+1}-1].

%I A092097 #12 Sep 24 2018 16:53:14
%S A092097 2,5,8,22,47,103,234,493,1087,2282,4901,10427,21993,46389,97394,
%T A092097 204567,427099,892587,1858338,3865692,8027140,16642918,34463760,
%U A092097 71273199,147235636,303814862,626313383,1289883519,2654196000
%N A092097 Limit number of (m-n)-almost-primes in range [2^m..2^{m+1}-1].
%C A092097 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 A092097 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 A092097 For n>0, a(n) = A052130(n+1)-A052130(n).
%e A092097 a(0) = 2: m-almost primes in [2^m..2^{m+1}-1] are 2^m and 3*2^{m-1}.
%e A092097 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 A092097 Cf. A052130, A001222, A026356, A120033-A120043.
%K A092097 easy,nonn
%O A092097 0,1
%A A092097 _Andrew S. Plewe_, Feb 19 2004
%E A092097 Edited and extended by _Franklin T. Adams-Watters_, Jun 20 2006