A092097 - OEIS

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

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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

LINKS

Table of n, a(n) for n=0..28.

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

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

Sequence in context: A177245 A283511 A137095 * A195295 A088144 A100501

Adjacent sequences: A092094 A092095 A092096 * A092098 A092099 A092100

KEYWORD

easy,nonn

AUTHOR

Andrew S. Plewe, Feb 19 2004

EXTENSIONS

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

STATUS

approved