

A115057


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


1



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
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OFFSET

1,1


COMMENTS

Numbers k such that Pi(2n1, (nth nalmost prime) * ((n+1)th (n+1)almostprime)) = Pi(2n1, A101695(n)*A101695(n+1)) = (2n1)AlmostPrime(k).


LINKS

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


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 *)


CROSSREFS

Cf. A101695.
Sequence in context: A220813 A217303 A053033 * A228344 A157421 A274830
Adjacent sequences: A115054 A115055 A115056 * A115058 A115059 A115060


KEYWORD

nonn,less


AUTHOR

Jonathan Vos Post, Oct 08 2007


STATUS

approved



