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A053810
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Prime powers of prime numbers.
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37
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4, 8, 9, 25, 27, 32, 49, 121, 125, 128, 169, 243, 289, 343, 361, 529, 841, 961, 1331, 1369, 1681, 1849, 2048, 2187, 2197, 2209, 2809, 3125, 3481, 3721, 4489, 4913, 5041, 5329, 6241, 6859, 6889, 7921, 8192, 9409, 10201, 10609, 11449, 11881, 12167
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OFFSET
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1,1
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COMMENTS
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This is to triprimes as A053810 (Prime powers of prime numbers) is to primes and as semiprimes are to A113877 (Semiprimes to semiprime powers). - Jonathan Vos Post, Mar 26 2013
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..9965
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FORMULA
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a(n) = A053811(n)^A053812(n). - David Wasserman, Feb 17 2006
A010055(a(n)) * A010051(A100995(a(n))) = 1. - Reinhard Zumkeller, Jun 05 2013
Sum_{n>=1} 1/a(n) = Sum_{p prime} P(p) = 0.6716752222..., where P is the prime zeta function. - Amiram Eldar, Nov 21 2020
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MATHEMATICA
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pp={}; Do[if=FactorInteger[n]; If[Length[if]==1&&PrimeQ[if[[1, 1]]]&&PrimeQ[if[[1, 2]]], pp=Append[pp, n]], {n, 13000}]; pp
Sort[ Flatten[ Table[ Prime[n]^Prime[i], {n, 1, PrimePi[ Sqrt[12800]]}, {i, 1, PrimePi[ Log[ Prime[n], 12800]]}]]]
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PROG
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(PARI) is(n)=isprime(isprimepower(n)) \\ Charles R Greathouse IV, Mar 19 2013
(Haskell)
a053810 n = a053810_list !! (n-1)
a053810_list = filter ((== 1) . a010051 . a100995) $ tail a000961_list
-- Reinhard Zumkeller, Jun 05 2013
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CROSSREFS
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Cf. A000040, A000961, A053811, A053812.
Cf. A203967; subsequence of A000961.
Sequence in context: A093771 A051676 A114129 * A076702 A051761 A153326
Adjacent sequences: A053807 A053808 A053809 * A053811 A053812 A053813
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley, Mar 28 2000
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EXTENSIONS
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More terms from David Wasserman, Feb 17 2006
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STATUS
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approved
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