|
| |
|
|
A115057
|
|
Number of (2n+1)-almost primes less than or equal to (n-th n-almost 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
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
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.
|
|
|
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 Weisstein (eww(AT)wolfram.com) 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 (rgwv(AT)rgwv.com), Oct 08 2007 *)
|
|
|
CROSSREFS
| Cf. A101695.
Sequence in context: A078894 A086319 A053033 * A157421 A038390 A048210
Adjacent sequences: A115054 A115055 A115056 * A115058 A115059 A115060
|
|
|
KEYWORD
| nonn,less
|
|
|
AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 08 2007
|
| |
|
|
