A119966 The n-almost primeth recurrence: a(0) = 1, a(n) = n-almostprime(a(n-1)).

1, 2, 6, 28, 220, 2565, 45846, 1268622, 55336336, 3876385680, 443603651136, 84205632289664

Offset: 0

Author

Jonathan Vos Post and Robert G. Wilson v, May 31 2006

Keywords

• nonn

Examples

			a(0)=1, a(1) is the first prime 2, a(2) is the second semiprime 6, a(3) is the sixth 3-almost prime 28, etc.
		

Crossrefs

Cf. A007097, A105999, A119965.

Programs

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 *)
AlmostPrime[k_Integer,n] = Block[{e = Floor[ Log[2, n] + 1], a, b}, a = 2^e; Do[b = 2^p; While[AlmostPrimePi[k, a] < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; a[n_] := a[n] = AlmostPrime[n, a[n - 1]]; a[0] = 1; Array[a, 11, 0] (* Robert G. Wilson v, Apr 14 2017 *)

Extensions

a(10)-a(11) from Donovan Johnson, Sep 18 2010