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 A225727 Numbers n such that sum of first n primorials (A143293) is divisible by n. 2
 1, 3, 17, 51, 967, 2901, 16439, 49317, 147951, 1331559 (list; graph; refs; listen; history; text; internal format)
 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 (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) A225727_list = list(islice(A225727_gen(), 6)) # Chai Wah Wu, Feb 23 2022 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

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Last modified February 27 16:21 EST 2024. Contains 370378 sequences. (Running on oeis4.)