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Search: id:A115057
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| A115057 |
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Number of (2n+1)-almost primes less than or equal to (n-th n-almost prime) * ((n+1)-th (n+1)-almostprime). |
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1
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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).
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LINKS
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Robert G. Wilson v, Table of n, a(n) for n = 1..228.
Eric Weisstein's World of Mathematics, Almost Prime.
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MATHEMATICA
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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@rgwv.com), Oct 08 2007 *)
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CROSSREFS
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Cf. A101695.
Sequence in context: A078894 A086319 A053033 this_sequence A038390 A048210 A023222
Adjacent sequences: A115054 A115055 A115056 this_sequence A115058 A115059 A115060
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KEYWORD
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nonn,less
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 08 2007
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