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 A225728 Primes p such that sum of primorials (A143293) not including p as a factor is divisible by p. 0
 3, 17, 967 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS EXAMPLE 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. 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, 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) s=P=1; forprime(p=2, 1e6, s+=P*=p; if(s%p==0, print1(p", "))) \\ Charles R Greathouse IV, Mar 19 2014 (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) A225728_list = list(islice(A225728_gen(), 3)) # Chai Wah Wu, Feb 23 2022 CROSSREFS Cf. A002110, A143293, A225727. Sequence in context: A270816 A217957 A252730 * A351590 A175984 A051710 Adjacent sequences: A225725 A225726 A225727 * A225729 A225730 A225731 KEYWORD nonn,bref,hard,more AUTHOR Alex Ratushnyak, May 14 2013 STATUS approved

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Last modified December 1 14:21 EST 2022. Contains 358468 sequences. (Running on oeis4.)