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Search: id:A114944
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| A114944 |
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Prime(n) + Semiprime(n) + 3AlmostPrime(n) + 4AlmostPrime(n). |
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+0
3
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| 30, 45, 68, 77, 106, 112, 118, 164, 176, 188, 204, 223, 243, 273, 286, 304, 319, 328, 350, 372, 385, 424, 439, 459, 479, 496, 511, 529, 544, 553, 580, 596, 626, 632, 668, 692, 730, 742, 753, 771, 781, 793, 823, 838, 857, 870, 887, 909, 929, 938, 974, 999
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Primes in this sequence include a(12) = 223, a(23) = 439, a(25) = 479, a(43) = 823, a(45) = 857, a(47) = 887, a(49) = 929.
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LINKS
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Eric Weisstein's World of Mathematics, Almost Prime.
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FORMULA
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a(n) = A000040(n) + A001358(n) + A014612(n) + A014613(n). a(n) = A014613(n) + A114382(n).
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EXAMPLE
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a(1) = Prime[1] + Semiprime[1] + 3AlmostPrime[1] + 4AlmostPrime[1] = 2 + 4 + 8 + 16 = 30.
a(6) = (Prime[6] + Semiprime[6] + 3AlmostPrime[6]) + 4AlmostPrime[6] =
A114382(6) + 4AlmostPrime[6] = 56 + 56 = 112.
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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
AlmostPrime[k_, n_] := Block[{e = Floor[Log[2, n]], a, b}, a = 2^e; Do[b = 2^p; While[AlmostPrimePi[k, a] < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; Table[ Sum[ AlmostPrime[k, n], {k, 4}], {n, 52}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Feb 21 2006)
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CROSSREFS
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Cf. A000040, A001358, A014612, A014613, A114382.
Sequence in context: A090692 A102843 A062385 this_sequence A075290 A004222 A004223
Adjacent sequences: A114941 A114942 A114943 this_sequence A114945 A114946 A114947
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Feb 20 2006
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