OFFSET
0,2
COMMENTS
A k-almost-prime is a positive integer that has exactly k prime factors, counted with multiplicity.
LINKS
Eric Weisstein's World of Mathematics, Almost Prime.
EXAMPLE
a(2) = 9 since 5^2 is the 9th 2-almost-prime: {4,6,9,10,14,15,21,22,25,...}.
MATHEMATICA
l = Table[0, {30}]; e = 0; Do[f = Plus @@ Last /@ FactorInteger[n]; l[[f+1]]++; If[n == 5^e, Print[l[[f+1]]]; e++ ], {n, 1, 5^10}] (* Ryan Propper, Aug 08 2005 *)
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 *)
Join[{1}, Table[ AlmostPrimePi[n, 5^n], {n, 1, 25}]] (* Robert G. Wilson v, Feb 10 2006 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre and Paul D. Hanna, Dec 10 2002
EXTENSIONS
a(8)-a(10) from Ryan Propper, Aug 08 2005
a(11)-a(25) from Robert G. Wilson v, Feb 10 2006
a(26) from Donovan Johnson, Sep 27 2010
STATUS
approved