1,2

Adolf Hildebrand, On the number of prime factors of an integer. Ramanujan revisited (Urbana-Champaign, Ill., 1987), 167 - 185, Academic Press, Boston, MA, 1988.

Edmund Georg Hermann Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Chelsea Publishing, NY 1953, pp. 205 - 211.

Jonathan Vos Post & Robert G. Wilson v, Table of n, a(n) for n = 1..1276

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (1).

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (2).

Triangle begins:

1

2 1

4 2 1

6 6 2 1

11 10 7 2 1

18 22 13 7 2 1

31 42 30 14 7 2 1

54 82 60 34 15 7 2 1

97 157 125 71 36 15 7 2 1

172 304 256 152 77 37 15 7 2 1

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[ AlmostPrimePi[m, 2^n], {n, 16}, {m, n}] // Flatten

First column: A007053, the last row reversed: A052130; the n-th row's sum: A000225 = 2^n -1.

Cf. A126280: same array but for powers of ten.

Sequence in context: A124840 A145118 A124927 this_sequence A135837 A027144 A158303

Adjacent sequences: A126276 A126277 A126278 this_sequence A126280 A126281 A126282

tabl,less,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com) & Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 22 2006