Search: id:A069098
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%I A069098
%S A069098 1,1,4,1,2,1,4,27,8,1,12,1,32,9,256,1,432,1,16,81,512,1,12,3125,2048,
%T A069098 19683,256,1,72,1,65536,6561,32768,25,1728,1,131072,59049,32,1,2592,1,
%U A069098 65536,135,2097152,1,6912,823543,800000
%N A069098 Number of minimal monic annihilator polynomials over the ring of integers 
               modulo n.
%H A069098 A. Vardy, <a href="a069098.txt">Comments and C program</a>
%F A069098 a(n) = 1 if n is prime.
%F A069098 Let n = prod_{i=1}^m p_i^e_i be the prime decomposition of n. For p prime 
               and integers k, q, define N(k, p, q) = p^{ sum_{j=0}^{k-1} b(j)} 
               where b(j) is the largest integer b in {0, 1, 2, ..., q } such that 
               p^b divides j!. Then a(n) = prod_{i=1}^m N(S(n), p_i, e_i) where 
               S(n) is the n-th Smarandache number (sequence A002034), i.e. S(n) 
               is the smallest integer k such that n divides k!. - Navin Kashyap 
               (nkashyap(AT)ece.ucsd.edu), Aug 07 2002
%e A069098 a(6)=2 because there are exactly two minimal annihilator polynomials 
               over Z_6, namely X^3 + 5x and X^3 + 3x^2 + 2x.
%Y A069098 Cf. A002034.
%Y A069098 Sequence in context: A030787 A109008 A074695 this_sequence A126241 A019777 
               A090885
%Y A069098 Adjacent sequences: A069095 A069096 A069097 this_sequence A069099 A069100 
               A069101
%K A069098 nonn,nice
%O A069098 2,3
%A A069098 Alexander Vardy (vardy(AT)montblanc.ucsd.edu), Apr 05 2002
%E A069098 More terms from Navin Kashyap (nkashyap(AT)ece.ucsd.edu), Aug 07 2002

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