Search: id:A060886
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%I A060886
%S A060886 1,1,13,73,241,601,1261,2353,4033,6481,9901,14521,20593,28393,38221,
%T A060886 50401,65281,83233,104653,129961,159601,194041,233773,279313,331201,
%U A060886 390001,456301,530713,613873,706441,809101,922561,1047553,1184833
%N A060886 n^4 - n^2 + 1.
%C A060886 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
%H A060886 Harry J. Smith, <a href="b060886.txt">Table of n, a(n) for n=0,...,1000</
               a>
%o A060886 (PARI) { for (n=0, 1000, write("b060886.txt", n, " ", n^4 - n^2 + 1); 
               ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 14 2009]
%Y A060886 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).
%Y A060886 Sequence in context: A142787 A084218 A125258 this_sequence A081586 A143008 
               A107963
%Y A060886 Adjacent sequences: A060883 A060884 A060885 this_sequence A060887 A060888 
               A060889
%K A060886 nonn
%O A060886 0,3
%A A060886 N. J. A. Sloane (njas(AT)research.att.com), May 05 2001

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