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Search: id:A128287
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| A128287 |
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Nonprime numbers n such that n divides A014137(n) = Partial sums of Catalan numbers (A000108). |
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+0
2
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OFFSET
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1,2
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COMMENT
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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.
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EXAMPLE
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A014137(n) begins {1, 2, 4, 9, 23, 65, 197, 626, 2056, 6918, 23714, 82500, ...}.
Thus a(1) = 1 because 1 is nonprime and divides A014137(1) = 2.
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.
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MATHEMATICA
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s = 1; Do[s = s + (2n)!/n!/(n+1)!; If[ !PrimeQ[n] && Mod[s, n] == 0, Print[n]], {n, 1000}]
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CROSSREFS
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Cf. A014137, A000108, A045309, A045309.
Sequence in context: A041112 A073701 A079912 this_sequence A003375 A007032 A069988
Adjacent sequences: A128284 A128285 A128286 this_sequence A128288 A128289 A128290
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KEYWORD
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bref,hard,more,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Feb 23 2007
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EXTENSIONS
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One more term from Ryan Propper (rpropper(AT)stanford.edu), Apr 02 2007
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