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A116433
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Consider the array T(r,c) where is the number of r-almost primes less than or equal to r^c, starting with a(0)=1. Read the array by antidiagonals.
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2
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0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 3, 1, 0, 1, 3, 6, 5, 1, 0, 1, 3, 9, 13, 8, 1, 0, 1, 4, 13, 30, 34, 14, 1, 0, 1, 4, 17, 50, 90, 77, 23, 1, 0, 1, 4, 22, 82, 200, 269, 177, 39, 1, 0, 1, 4, 26, 125, 385, 726, 788, 406, 64, 1, 0, 1, 5, 34, 181, 669, 1688, 2613, 2249, 887, 103, 1, 0, 1, 5
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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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
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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 Weisstein (eww(AT)wolfram.com) Feb 07 2006
Table[ If[k == 0, 1, AlmostPrimePi[n - k + 1, k^(n - k + 1)]], {n, 0, 7}, {k, n, 0, -1}] // Flatten
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CROSSREFS
| Cf. The rows are: A000004, A000012, A078843, A116426, A078844, A116427, A078845, A116428, A116429, A116430, A078846, A116431.
The columns are: A057427, A000720.
Sequence in context: A114219 A119339 A037835 * A106509 A196199 A053615
Adjacent sequences: A116430 A116431 A116432 * A116434 A116435 A116436
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 15 2006
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