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A051674
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a(n) = prime(n)^prime(n).
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105
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4, 27, 3125, 823543, 285311670611, 302875106592253, 827240261886336764177, 1978419655660313589123979, 20880467999847912034355032910567, 2567686153161211134561828214731016126483469
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OFFSET
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1,1
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COMMENTS
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n such that bigomega(n)^(bigomega(n)) = n, where bigomega = A001222. - Lekraj Beedassy, Aug 21 2004
Positive n such that n' = n, where n' is the arithmetic derivative of n. - T. D. Noe, Oct 12 2004
David Beckwith proposes (in the AMM reference): "Let n be a positive integer and let p be a prime number. Prove that (p^p) | n! implies that (p^(p + 1)) | n!". - Jonathan Vos Post, Feb 20 2006
Subsequence of A100716; A003415(m*a(n)) = A129283(m)*a(n), especially A003415(a(n)) = a(n). - Reinhard Zumkeller, Apr 07 2007
A168036(a(n)) = 0. - Reinhard Zumkeller, May 22 2015
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REFERENCES
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J.-M. De Koninck & A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 740 pp. 95; 312, Ellipses Paris 2004.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..40
David Beckwith, Problem 11158, American Mathematical Monthly, Vol. 112, No. 5 (May 2005), p. 468.
Jurij Kovic, The Arithmetic Derivative and Antiderivative, Journal of Integer Sequences, Vol. 15 (2012), #12.3.8.
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FORMULA
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a(n) = A000312(A000040(n)). - Altug Alkan, Sep 01 2016
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EXAMPLE
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a(1) = 2^2 = 4.
a(2) = 3^3 = 27.
a(3) = 5^5 = 3125.
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MAPLE
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A051674:=n->ithprime(n)^ithprime(n): seq(A051674(n), n=1..10); # Wesley Ivan Hurt, Jun 25 2016
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MATHEMATICA
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Array[Prime[ # ]^Prime[ # ] &, 12] (* Vladimir Joseph Stephan Orlovsky, May 01 2008 *)
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PROG
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(Haskell)
a051674_list = map (\p -> p ^ p) a000040_list
-- Reinhard Zumkeller, Jan 21 2012
(PARI) a(n)=n=prime(n); n^n \\ Charles R Greathouse IV, Mar 20 2013
(MAGMA) [p^p: p in PrimesUpTo(30)]; // Vincenzo Librandi, Mar 27 2014
(Python) from gmpy2 import mpz
[mpz(prime(n))**mpz(prime(n)) for n in range(1, 100)] # Chai Wah Wu, Jul 28 2014
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CROSSREFS
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Cf. A000040, A000312, A003415 (arithmetic derivative of n), A129150, A129151, A129152, A048102, A072873 (multiplicative closure), A104126.
Subsequence of A100717; A203908(a(n)) = 0.
Subsequence of A097764.
Cf. A168036, A094289 (decimal expansion of Sum(1/p^p)).
Sequence in context: A066352 A249105 A249110 * A132641 A008973 A132646
Adjacent sequences: A051671 A051672 A051673 * A051675 A051676 A051677
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KEYWORD
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nonn,easy
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AUTHOR
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Asher Auel (asher.auel(AT)reed.edu)
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STATUS
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approved
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