|
%I #18 Feb 23 2022 11:36:14
%S 1,3,17,51,967,2901,16439,49317,147951,1331559
%N Numbers n such that sum of first n primorials (A143293) is divisible by n.
%C a(5) = 967 is a prime,
%C a(6) = a(5) * 3,
%C a(7) = a(5) * 17,
%C a(8) = a(5) * 51,
%C a(9) = a(5) * 51 * 3,
%C a(10) = a(5) * 51 * 27.
%C The next term, if it exists, is greater than 15600000. - _Alex Ratushnyak_, Jun 16 2013
%e Sum of first 3 primorials is 1+2+6=9, because 9 is divisible by 3, the latter is in the sequence.
%e Sum of first 17 primorials is A143293(17) = 1955977793053588026279. Because A143293(17) 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(5,10000000,6):
%o addPrime(n)
%o addPrime(n+2)
%o sum = 0
%o primorial = n = 1
%o for p in primes:
%o sum += primorial
%o primorial *= p
%o if sum % n == 0: print n,
%o n += 1
%o (Python)
%o from itertools import chain, accumulate, count, islice
%o from operator import mul
%o from sympy import prime
%o 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)
%o A225727_list = list(islice(A225727_gen(),6)) # _Chai Wah Wu_, Feb 23 2022
%Y Cf. A143293, A002110, A057245, A128981.
%K nonn,hard,more
%O 1,2
%A _Alex Ratushnyak_, May 13 2013
|
