

A128287


Nonprime numbers n such that n divides A014137(n) = Partial sums of Catalan numbers (A000108).


1




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*i2)//(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 A003375 A007032
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



