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A060886
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n^4 - n^2 + 1.
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20
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1, 1, 13, 73, 241, 601, 1261, 2353, 4033, 6481, 9901, 14521, 20593, 28393, 38221, 50401, 65281, 83233, 104653, 129961, 159601, 194041, 233773, 279313, 331201, 390001, 456301, 530713, 613873, 706441, 809101, 922561, 1047553, 1184833
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OFFSET
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0,3
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COMMENTS
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All positive divisors of a(n) are congruent to 1, modulo 12. Proof: If p is an odd prime different from 3 then n^4 - n^2 + 1 = 0 (mod p) implies: (a) (2n^2 - 1)^2 = -3 (mod p), whence p = 1 (mod 6); and (b) (n^2 - 1)^2 = -n^2 (mod p), whence p = 1 (mod 4). - Nick Hobson Nov 13 2006
Appears to be the number of distinct possible sums of a set of n distinct integers between 1 and n^3. checked up to n=4. [From Dylan Hamilton, Sep 21 2010]
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,1000
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FORMULA
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G.f.: (1-4*x+18*x^2+8*x^3+x^4)/(1-x)^5. [Colin Barker, Apr 21 2012]
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PROG
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(PARI) { for (n=0, 1000, write("b060886.txt", n, " ", n^4 - n^2 + 1); ) } [From Harry J. Smith, Jul 14 2009]
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CROSSREFS
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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).
Sequence in context: A084218 A175361 A125258 * A081586 A143008 A107963
Adjacent sequences: A060883 A060884 A060885 * A060887 A060888 A060889
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, May 05 2001
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STATUS
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approved
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