

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

Table of n, a(n) for n=1..10.


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


CROSSREFS

Cf. A143293, A002110, A057245, A128981.
Sequence in context: A011917 A018691 A332869 * A163943 A093418 A173733
Adjacent sequences: A225724 A225725 A225726 * A225728 A225729 A225730


KEYWORD

nonn,hard,more


AUTHOR

Alex Ratushnyak, May 13 2013


STATUS

approved



