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1, 2, 17, 82, 257, 626, 1297, 2402, 4097, 6562, 10001, 14642, 20737, 28562, 38417, 50626, 65537, 83522, 104977, 130322, 160001, 194482, 234257, 279842, 331777, 390626, 456977, 531442, 614657, 707282
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OFFSET
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0,2
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COMMENTS
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Let Phi_k(x) be the k-th cyclotomic polynomial and form the sequence Phi_k(0), Phi_k(1), Phi_k(2), ... This gives A000027 (k=2), A002061 (k=3), A002522 (k=4), A053699 (k=5), A002061 (k=6), A053716 (k=7), A002523 (k=8), A060883 (k=9), A060884 (k=10), A060885 (k=11), A060886 (k=12), A060887 (k=13), A060888 (k=14), A060889 (k=15), A060890 (k=16), A060891 (k=18), A060892 (k=20), A060893 (k=24), A060894 (k=30), A060895 (k=32), A060896 (k=36).
All odd prime factors of a(n) are congruent to 1 modulo 8. - Nick Hobson Jan 14 2007
Lee and Murty, p. 685: "In spite of these remarkable advances, we are still unable to determine if n^4 + 1 is infinitely often a squarefree number". - Jonathan Vos Post, Sep 18 2007
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REFERENCES
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Jung-Jo Lee and M. Ram Murty, "Dirichlet series and hyperelliptic curves", Forum Math. 19(2007), 677-705.
Mabkhout, M. (1993). "Minoration de P(x4+1)". Rend. Sem. Fac. Sci. Univ. Cagliari 63 (2): 135-148.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for sequences related to linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
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O.g.f.: (1-3*x+17*x^2+7*x^3+2*x^4)/(1-x)^5 . a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) - R. J. Mathar, Apr 28 2008
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MATHEMATICA
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Table[n^4+1, {n, 0, 60}] (* From Vladimir Joseph Stephan Orlovsky, Apr 15 2011 *)
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PROG
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(MAGMA) [n^4 + 1: n in [0..40]]; // Vincenzo Librandi, Jun 07 2011
(Maxima) A002523(n):=n^4+1$ makelist(A002523(n), n, 0, 30); /* Martin Ettl, Nov 07 2012 */
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CROSSREFS
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Cf. A005117.
Sequence in context: A183175 A060352 A215185 * A079889 A053786 A181546
Adjacent sequences: A002520 A002521 A002522 * A002524 A002525 A002526
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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