OFFSET
0,8
EXAMPLE
The array begins:
0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1
1 2 3 5 8 14 23 39 64 103 169
1 2 6 13 34 77 177 406 887 1962 4225
1 3 9 30 90 269 788 2249 6340 17526 47911
T(3,2)=3 because there are 3 2-almost primes <= 3^2 = 9, namely 4, 6, and 9 (see A001358).
MATHEMATICA
AlmostPrimePi[k_Integer, n_] := Module[{a, i}, a[0] = 1; If[k == 1, PrimePi[n], Sum[PrimePi[n/Times @@ Prime[Array[a, k - 1]]] - a[k - 1] + 1, Evaluate[ Sequence @@ Table[{a[i], a[i - 1], PrimePi[(n/Times @@ Prime[Array[a, i - 1]])^(1/(k - i + 1))]}, {i, k - 1}]] ]]]; (* Eric W. Weisstein, Feb 07 2006 *)
Table[ If[k == 0, 1, AlmostPrimePi[n - k + 1, k^(n - k + 1)]], {n, 0, 7}, {k, n, 0, -1}] // Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna and Robert G. Wilson v, Feb 15 2006
EXTENSIONS
NAME corrected by R. J. Mathar, Jun 20 2021
STATUS
approved