OFFSET
1,2
COMMENTS
A052130: For m very large, a(n) = number of numbers between 1 and 2^m with m-n prime factors (counted with multiplicity).
In observing the triangular array of A126279, the array T(k,n) defined as the k-th almost prime count of n-th power of two, it is noticed that the k-th term from the right converges to a fixed value beginning with the n-th power of two.
Will this sequence continue to match A117630: floor(n*log(3)/log(3/2)) ?
LINKS
J. H. Smith, Perfect Numbers.
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}]] ]]]; f[n_] := Block[{a = 0, m = n}, While[ b = AlmostPrimePi[m-n+1, 2^m]; b > a, m++; a = b]; m--; m]; Array[f, 24] (* Eric W. Weisstein, Feb 07 2006 *)
CROSSREFS
KEYWORD
more,nonn
AUTHOR
Robert G. Wilson v, Dec 24 2006
EXTENSIONS
a(25)-a(28) from Robert G. Wilson v, Sep 07 2012
Expression in comment corrected by L. Edson Jeffery, Apr 03 2015
STATUS
approved