Search: id:A089631
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%I A089631
%S A089631 0,1,0,1,0,1,0,1,2,1,0,1,2,7,0,1,0,1,2,9,2,1,0,1,2,1,2,1,6,1,0,13,2,11,
%T A089631 0,1,2,15,2,1,6,1,2,7,2,1,0,1,2,19,2,1,0,15,2,21,2,1,6,1,2,9,0,17,6,1,
               2,
%U A089631 25,22,1,0,1,2,7,2,17,6,1,2,1,2,1,6,21,2,31,2,1,6,19,2,33,2,23,0,1,2,13
%N A089631 a(n) = (Product_{p is a prime factor of n} p)) mod (Product_{p is a prime 
               factor of n} p-1).
%C A089631 It can be shown that the unsolved problem of finding a composite solution 
               n of the congruence n-1 = 1 mod phi(n) is equivalent to finding a 
               square-free composite number n such a(n) = 1.
%H A089631 C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_248.htm">
               Puzzle 248, The Prime Puzzles and Problems Connection</a>
%e A089631 Let n = 10; then Product_{p is a prime factor of 10} p = 2 x 5 = 10, 
               Product_{p is a prime factor of 10} p-1 = (2-1) x (5-1) = 10.
%t A089631 p[n_] := Transpose[FactorInteger[n]][[1]]; t = Table[p[i], {i, 2, 100}]; 
               r = {}; s = {}; For[i = 1, i <= 99, i++, r = Append[r, Product[t[[i]][[j]], 
               {j, 1, Length[t[[i]]]}]]; s = Append[s, Product[t[[i]][[j]] - 1, 
               {j, 1, Length[t[[i]]]}]]]; Mod[r, s]
%Y A089631 Sequence in context: A129620 A074766 A138107 this_sequence A129558 A131185 
               A052249
%Y A089631 Adjacent sequences: A089628 A089629 A089630 this_sequence A089632 A089633 
               A089634
%K A089631 nonn
%O A089631 2,9
%A A089631 Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 04 2004

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