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A114791 Consider the array T where the element at T(r,c) is the number of n-almost primes less than or equal to 2^m. Sequence read by successive columns beginning at r=c. 0
1, 1, 2, 1, 2, 4, 1, 2, 6, 6, 1, 2, 7, 10, 11, 1, 2, 7, 13, 22, 18, 1, 2, 7, 14, 30, 42, 31, 1, 2, 7, 15, 34, 60, 82, 54, 1, 2, 7, 15, 36, 71, 125, 157, 97, 1, 2, 7, 15, 37, 77, 152, 256, 304, 172, 1, 2, 7, 15, 37, 81, 168, 325, 513, 589, 309, 1, 2, 7, 15, 37, 83, 177, 367, 669, 1049 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Eventually each column reads 1,2,7,15,37,84,187,421,914,... = A052130.

LINKS

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

FORMULA

Each column sums to 2^n-1.

EXAMPLE

1 2 4 6 11 18 31 54 97 172 309 564 1028 1900 3512 6542

..1 2 6 10 22 42 82 157 304 589 1124 2186 4192 8110 15658

....1 2 7 13 30 60 125 256 513 1049 2082 4214 8401 16771

......1 2 7 14 34 71 152 325 669 1405 2866 5931 12139

........1 2 7 15 36 77 168 367 770 1643 3410 7150

..........1 2 7 15 37 81 177 392 831 1790 3757

............1 2 7 15 37 83 182 406 867 1880

..............1 2 7 15 37 84 185 414 887

................1 2 7 15 37 84 186 418

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[ AlmostPrimePi[n, 2^k], {k, 12}, {n, k, 1, -1}] // Flatten

CROSSREFS

First row is A007053, Cf. A052130.

Sequence in context: A212829 A210215 A203647 * A129994 A208755 A226441

Adjacent sequences:  A114788 A114789 A114790 * A114792 A114793 A114794

KEYWORD

nonn,tabl

AUTHOR

Robert G. Wilson v, Feb 21 2006

STATUS

approved

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Last modified July 2 18:27 EDT 2022. Contains 355029 sequences. (Running on oeis4.)