A115057 Number of (2n+1)-almost primes less than or equal to (n-th n-almost prime) * ((n+1)-th (n+1)-almostprime).

2, 5, 11, 17, 25, 30, 45, 67, 74, 82, 95, 111, 141, 177, 193, 208, 211, 223, 257, 277, 288, 353, 431, 453, 481, 509, 528, 540, 563, 619, 672, 700, 725, 745, 804, 857, 905, 1003, 1077, 1127, 1199, 1268, 1281, 1321, 1354, 1379, 1423, 1517, 1607, 1660, 1714, 1748

Offset: 1

Author

Jonathan Vos Post, Oct 08 2007

Keywords

• nonn
• less

Comments

Numbers k such that Pi(2n-1, (n-th n-almost prime) * ((n+1)-th (n+1)-almostprime)) = Pi(2n-1, A101695(n)*A101695(n+1)) = (2n-1)-AlmostPrime(k).

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..228.
• Eric Weisstein's World of Mathematics, Almost Prime.

Crossrefs

Cf. A101695.

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 *);
lst={ (* the list of entries in A101695 *) }; lsu = {}; Do[a = AlmostPrimePi[2 n + 1, lst[[n]]*lst[[n + 1]]]; AppendTo[lsu, a]; Print[{n, a}], {n, 228}] (* Robert G. Wilson v, Oct 08 2007 *)