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A128287 Nonprime numbers n such that n divides A014137(n) = Partial sums of Catalan numbers (A000108). 1
1, 8, 133, 49378 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

a(5) > 5000000. - Chai Wah Wu, Nov 13 2014

LINKS

Table of n, a(n) for n=1..4.

EXAMPLE

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.

MATHEMATICA

s = 1; Do[s = s + (2n)!/n!/(n+1)!; If[ !PrimeQ[n] && Mod[s, n] == 0, Print[n]], {n, 1000}]

PROG

(Python)

from __future__ import division

from sympy import isprime

A128287_list, x, s = [1], 1, 2

for i in range(2, 10**5):

....x = x*(4*i-2)//(i+1)

....s += x

....if not (isprime(i) or s % i):

........A128287_list.append(i) # Chai Wah Wu, Nov 13 2014

CROSSREFS

Cf. A014137, A000108, A045309, A045309.

Sequence in context: A237026 A079912 A281948 * A221545 A316177 A003375

Adjacent sequences:  A128284 A128285 A128286 * A128288 A128289 A128290

KEYWORD

bref,hard,more,nonn

AUTHOR

Alexander Adamchuk, Feb 23 2007

EXTENSIONS

One more term from Ryan Propper, Apr 02 2007

STATUS

approved

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Last modified October 22 13:06 EDT 2018. Contains 316459 sequences. (Running on oeis4.)