The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #13 Jan 28 2022 00:55:46
%S 2,2,2,2,4,2,5,4,5,2,7,12,6,5,2,13,20,17,7,5,2,23,40,30,20,8,5,2,43,
%T 75,65,37,21,8,5,2,75,147,131,81,41,22,8,5,2,137,285,257,173,91,44,22,
%U 8,5,2,255,535,536,344,199,96,46,22,8,5,2,464,1062,1033,736,403,215,99,47
%N Triangle read by rows: T(n,k) is number of numbers x, 2^n <= x < 2^(n+1), with k prime factors (counted with multiplicity).
%C Sequence A092097 gives the limiting behavior at the end of the rows. - _T. D. Noe_, Feb 22 2008
%H T. D. Noe, <a href="/A037088/b037088.txt">Rows n=1..24 of triangle, flattened</a>
%e The triangular array begins 2; 2,2; 2,4,2; 5,4,5,2; 7,12,6,5,2; ...
%e a(7) = 5 because the 3-almost primes between 16 and 32 are (18,20,27,28,30).
%t t[n_, k_] := Count[Range[2^n, 2^(n+1)-1], x_ /; Total[FactorInteger[x][[All, 2]]] == k]; Table[t[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Nov 07 2013 *)
%Y A001222 counts factors of n. A000040, A001358, A014612-A014614 are special cases. A036378 and A025488 are applications of binary order A029837. Leading diagonal is essentially A036378 and has partial sums A007053.
%K nonn,tabl,nice
%O 1,1
%A _Alford Arnold_
%E More terms from _Naohiro Nomoto_, Jun 18 2001