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

2, 5, 8, 22, 47, 103, 234, 493, 1087, 2282, 4901, 10427, 21993, 46389, 97394, 204567, 427099, 892587, 1858338, 3865692, 8027140, 16642918, 34463760, 71273199, 147235636, 303814862, 626313383, 1289883519, 2654196000

Offset: 0

Author

Andrew S. Plewe, Feb 19 2004

Keywords

• easy
• nonn

Comments

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

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

Examples

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

Crossrefs

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

Formula

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

Extensions

Edited and extended by Franklin T. Adams-Watters, Jun 20 2006