

A037088


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).


3



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, 75, 65, 37, 21, 8, 5, 2, 75, 147, 131, 81, 41, 22, 8, 5, 2, 137, 285, 257, 173, 91, 44, 22, 8, 5, 2, 255, 535, 536, 344, 199, 96, 46, 22, 8, 5, 2, 464, 1062, 1033, 736, 403, 215, 99, 47
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OFFSET

1,1


COMMENTS

Sequence A092097 gives the limiting behavior at the end of the rows.  T. D. Noe, Feb 22 2008


LINKS



EXAMPLE

The triangular array begins 2; 2,2; 2,4,2; 5,4,5,2; 7,12,6,5,2; ...
a(7) = 5 because the 3almost primes between 16 and 32 are (18,20,27,28,30).


MATHEMATICA

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 (* JeanFrançois Alcover, Nov 07 2013 *)


CROSSREFS



KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



