%I
%S 3,17,967
%N Primes p such that sum of primorials (A143293) not including p as a factor is divisible by p.
%C As in A002110, primorial(0)=1, and primorial(n) = primorial(n1)*prime(n).
%C The next term, if it exists, is bigger than 10^8.
%e Sum of primorials not including 3 as a factor is 1 + 2 = 3. Because it's divisible by 3, the latter is in the sequence.
%e Sum of primorials not including 17 as a factor is 1 + 2 + 6 + 6*5 + 30*7 + 210*11 + 2310*13 = 32589. Because 32589 is divisible by 17, the latter is in the sequence.
%o (Python)
%o primes = [2]*2
%o primes[1] = 3
%o def addPrime(k):
%o for p in primes:
%o if k%p==0: return
%o if p*p > k: break
%o primes.append(k)
%o for n in range(5,100000000,6):
%o addPrime(n)
%o addPrime(n+2)
%o sum = 0
%o primorial = 1
%o for p in primes:
%o sum += primorial
%o primorial *= p
%o if sum % p == 0: print p,
%o (PARI) s=P=1;forprime(p=2,1e6,s+=P*=p;if(s%p==0,print1(p", "))) \\ _Charles R Greathouse IV_, Mar 19 2014
%o (PARI) is(p)=if(!isprime(p),return(0)); my(s=Mod(1,p),P=s); forprime(q=2,p1,s+=P*=q); s==0 \\ _Charles R Greathouse IV_, Mar 19 2014
%Y Cf. A002110, A143293, A225727.
%K nonn,bref,hard,more
%O 1,1
%A _Alex Ratushnyak_, May 14 2013
