A126281 a(n) is the least m to satisfy the requirements of A052130.

1, 2, 5, 8, 10, 13, 16, 18, 21, 24, 27, 29, 32, 35, 37, 40, 43, 46, 48, 51, 54, 56, 59, 62, 65, 67, 70, 73

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

Table of n, a(n) for n=1..28.

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

Cf. A052130, A126279.

Sequence in context: A189535 A330214 A182769 * A117630 A284774 A309095

Adjacent sequences: A126278 A126279 A126280 * A126282 A126283 A126284

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