

A225727


Numbers n such that sum of first n primorials (A143293) is divisible by n.


2




OFFSET

1,2


COMMENTS

a(5) = 967 is a prime,
a(6) = a(5) * 3,
a(7) = a(5) * 17,
a(8) = a(5) * 51,
a(9) = a(5) * 51 * 3,
a(10) = a(5) * 51 * 27.
The next term, if it exists, is greater than 15600000.  Alex Ratushnyak, Jun 16 2013


LINKS



EXAMPLE

Sum of first 3 primorials is 1+2+6=9, because 9 is divisible by 3, the latter is in the sequence.
Sum of first 17 primorials is A143293(17) = 1955977793053588026279. Because A143293(17) is divisible by 17, the latter is in the sequence.


PROG

(Python)
primes = [2]*2
primes[1] = 3
def addPrime(k):
for p in primes:
if k%p==0: return
if p*p > k: break
primes.append(k)
for n in range(5, 10000000, 6):
addPrime(n)
addPrime(n+2)
sum = 0
primorial = n = 1
for p in primes:
sum += primorial
primorial *= p
if sum % n == 0: print n,
n += 1
(Python)
from itertools import chain, accumulate, count, islice
from operator import mul
from sympy import prime
def A225727_gen(): return (i+1 for i, m in enumerate(accumulate(accumulate(chain((1, ), (prime(n) for n in count(1))), mul))) if m % (i+1) == 0)


CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR



STATUS

approved



