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Nonprime numbers k such that k divides A014137(k).
1

%I #15 Jun 13 2021 15:33:36

%S 1,8,133,49378

%N Nonprime numbers k such that k divides A014137(k).

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

%C a(5) > 5000000. - _Chai Wah Wu_, Nov 13 2014

%e 1 is nonprime and divides A014137(1) = 2, so 1 is a term.

%e 8 is nonprime and divides A014137(8) = 2056, so 8 is a term.

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

%o (Python)

%o from __future__ import division

%o from sympy import isprime

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

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

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

%o ....s += x

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

%o ........A128287_list.append(i) # _Chai Wah Wu_, Nov 13 2014

%Y Cf. A014137, A000108, A045309, A045309.

%K bref,hard,more,nonn

%O 1,2

%A _Alexander Adamchuk_, Feb 23 2007

%E One more term from _Ryan Propper_, Apr 02 2007