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

Author

Robert G. Wilson v, Dec 24 2006

Keywords

• more
• nonn

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.

Crossrefs

Cf. A052130, A126279.

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}]] ]]]; 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 *)

Extensions

a(25)-a(28) from Robert G. Wilson v, Sep 07 2012

Expression in comment corrected by L. Edson Jeffery, Apr 03 2015