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A225728
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Primes p such that sum of primorials (A143293) not including p as a factor is divisible by p.
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0
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OFFSET
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1,1
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COMMENTS
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As in A002110, primorial(0)=1, and primorial(n) = primorial(n-1)*prime(n).
The next term, if it exists, is bigger than 10^8.
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LINKS
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EXAMPLE
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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.
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.
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PROG
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(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, 100000000, 6):
addPrime(n)
addPrime(n+2)
sum = 0
primorial = 1
for p in primes:
sum += primorial
primorial *= p
if sum % p == 0: print p,
(PARI) is(p)=if(!isprime(p), return(0)); my(s=Mod(1, p), P=s); forprime(q=2, p-1, s+=P*=q); s==0 \\ Charles R Greathouse IV, Mar 19 2014
(Python)
from itertools import chain, accumulate, count, islice
from operator import mul
from sympy import prime
def A225728_gen(): return (prime(i+1) for i, m in enumerate(accumulate(accumulate(chain((1, ), (prime(n) for n in count(1))), mul))) if m % prime(i+1) == 0)
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CROSSREFS
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KEYWORD
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nonn,bref,hard,more
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AUTHOR
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STATUS
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approved
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