A128287 Nonprime numbers k such that k divides A014137(k).

1, 8, 133, 49378

Offset: 1

Author

Alexander Adamchuk, Feb 23 2007

Keywords

• bref
• hard
• more
• nonn

Comments

Prime p divides A014137(p) for p in A045309 (primes congruent to {0, 2} mod 3).

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

Examples

			1 is nonprime and divides A014137(1) = 2, so 1 is a term.
8 is nonprime and divides A014137(8) = 2056, so 8 is a term.
		

Crossrefs

Cf. A014137, A000108, A045309, A045309.

Programs

Mathematica

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

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

Extensions

One more term from Ryan Propper, Apr 02 2007