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A078845
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Where 7^n occurs in n-almost-primes, starting at a(0)=1.
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12
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1, 4, 17, 82, 385, 1688, 7089, 28893, 115180, 450906, 1740244, 6640747, 25115604, 94312569, 352110321, 1308256678, 4841115048, 17852264639, 65636109307, 240689877440, 880582139867
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OFFSET
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0,2
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COMMENTS
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A k-almost-prime is a positive integer that has exactly k prime factors, counted with multiplicity.
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LINKS
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Table of n, a(n) for n=0..20.
Eric Weisstein's World of Mathematics, Almost Prime.
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EXAMPLE
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a(2) = 17 since 7^2 is the 17th 2-almost-prime: {4,6,9,10,14,15,21,22,25,26,33,34,35,38,39,46,49,...}.
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MATHEMATICA
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l = Table[0, {30}]; e = 0; Do[f = Plus @@ Last /@ FactorInteger[n]; l[[f+1]]++; If[n == 7^e, Print[l[[f+1]]]; e++ ], {n, 1, 7^10}] (* Ryan Propper, Aug 08 2005 *)
AlmostPrimePi[k_Integer /; k > 1, n_] := Module[{a, i}, a[0] = 1; 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 *)
Table[ AlmostPrimePi[n, 7^n], {n, 2, 15}] (* Robert G. Wilson v, Feb 09 2006 *)
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CROSSREFS
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Cf. A078840, A078841, A078842, A078843, A078844, A078846.
Sequence in context: A151250 A174810 A121545 * A230126 A181517 A110771
Adjacent sequences: A078842 A078843 A078844 * A078846 A078847 A078848
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre and Paul D. Hanna, Dec 10 2002
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EXTENSIONS
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a(7)-a(10) from Ryan Propper, Aug 08 2005
a(11)-a(15) from Robert G. Wilson v, Feb 09 2006
a(16)-a(20) from Donovan Johnson, Sep 27 2010
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STATUS
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approved
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