Search: id:A128287
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%I A128287
%S A128287 1,8,133,49378
%N A128287 Nonprime numbers n such that n divides A014137(n) = Partial sums of Catalan 
               numbers (A000108).
%C A128287 Prime p divides A014137(p) for p = {2, 3, 5, 11, 17, 23, 29, 41, 47, 
               53, 59, 71, 83, 89, 101, ...} = A045309 Primes congruent to {0, 2} 
               mod 3 = A045309 Primes p such that x^3 = n (integer) has only one 
               solution mod p.
%e A128287 A014137(n) begins {1, 2, 4, 9, 23, 65, 197, 626, 2056, 6918, 23714, 82500, 
               ...}.
%e A128287 Thus a(1) = 1 because 1 is nonprime and divides A014137(1) = 2.
%e A128287 a(2) = 8 because 8 is nonprime and divides A014137(8) = 2056 and A014137(n) 
               is not divisible by any nonprime n for 1<n<8.
%t A128287 s = 1; Do[s = s + (2n)!/n!/(n+1)!; If[ !PrimeQ[n] && Mod[s, n] == 0, 
               Print[n]], {n, 1000}]
%Y A128287 Cf. A014137, A000108, A045309, A045309.
%Y A128287 Sequence in context: A041112 A073701 A079912 this_sequence A003375 A007032 
               A069988
%Y A128287 Adjacent sequences: A128284 A128285 A128286 this_sequence A128288 A128289 
               A128290
%K A128287 bref,hard,more,nonn
%O A128287 1,2
%A A128287 Alexander Adamchuk (alex(AT)kolmogorov.com), Feb 23 2007
%E A128287 One more term from Ryan Propper (rpropper(AT)stanford.edu), Apr 02 2007

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