

A197871


Irregular triangle T(n,k) of the number of numbers with k prime factors (repetitions allowed) less than n^2.


0



0, 2, 1, 4, 3, 1, 6, 6, 2, 1, 9, 9, 4, 2, 11, 13, 7, 3, 1, 15, 17, 10, 4, 2, 18, 22, 13, 7, 2, 1, 22, 26, 19, 8, 4, 1, 25, 34, 22, 12, 4, 2, 30, 40, 28, 13, 7, 2, 34, 48, 32, 18, 7, 3, 1, 39, 56, 38, 21, 9, 4, 1, 44, 62, 48, 24, 11, 4, 2, 48, 75, 51, 29, 13, 6, 2
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OFFSET

1,2


REFERENCES

G. J. O. Jameson, The Prime Number Theorem, Cambridge, 2004, p.145.


LINKS

Table of n, a(n) for n=1..76.


EXAMPLE

In the third row, reading from the left, 6 is the number of primes <= 16, 6 is the number of semiprimes <= 16, 2 is the number of numbers with three prime divisors (repetitions allowed) <= 16, and 1 is the number of numbers with four divisors <= 16. Triangle:
0
2 1
4 3 1
6 6 2 1
9 9 4 2
11 13 7 3 1
15 17 10 4 2


MATHEMATICA

Join[{0}, Flatten[Table[Transpose[Tally[Table[Plus @@ Last /@ FactorInteger[i], {i, 2, n^2}]]][[2]], {n, 2, 15}]]]


CROSSREFS

Similar to A052130.
Sequence in context: A187883 A134543 A305540 * A093010 A179000 A210559
Adjacent sequences: A197868 A197869 A197870 * A197872 A197873 A197874


KEYWORD

nonn,tabf


AUTHOR

Daniel Tisdale, Oct 18 2011


STATUS

approved



