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A092097
Limit number of (m-n)-almost-primes in range [2^m..2^{m+1}-1].
3
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
0,1
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
FORMULA
For n>0, a(n) = A052130(n+1)-A052130(n).
EXAMPLE
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
KEYWORD
easy,nonn
AUTHOR
Andrew S. Plewe, Feb 19 2004
EXTENSIONS
Edited and extended by Franklin T. Adams-Watters, Jun 20 2006
STATUS
approved