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 A225841 Numbers n such that the sum of first n primorial numbers is divisible by n. 0
 1, 2, 4, 523, 1046, 2092 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The k-th primorial number is defined as the product of the first k primes. The next term, if it exists, is greater than 14000000. - Alex Ratushnyak, Jun 13 2013 If a prime p | a(n) for some n, then p = 2, p = 523, or p > 10^8. Any such prime is itself a member of this sequence. From this (and a small amount of additional calculation) it follows that any other terms below 10^10 are of the form 2^k * p for p > 10^8. - Charles R Greathouse IV, Feb 09 2014 LINKS EXAMPLE 2 + 2*3 + 2*3*5 + 2*3*5*7 = 2 + 6 + 30 + 210 = 248, because 248 is divisible by 4, the latter is in the sequence. MATHEMATICA With[{nn=2100}, Select[Thread[{Accumulate[FoldList[Times, Prime[ Range[ nn]]]], Range[nn]}], Divisible[ #[[1]], #[[2]]]&]][[All, 2]] (* Harvey P. Dale, Jul 29 2021 *) PROG (Python) primes = [] n = 1 sum = 2 primorial = 6 def addPrime(k):   global n, sum, primorial   for p in primes:     if k%p==0:  return     if p*p > k:  break   primes.append(k)   sum += primorial   primorial *= k   n += 1   if sum % n == 0:  print(n, end=', ') print(1, end=', ') for p in range(5, 100000, 6):   addPrime(p)   addPrime(p+2) (PARI) list(maxx)={n=prime(1); cnt=1; summ=0; scnt=0; while(n<=maxx, summ=summ+prodeuler(x=1, prime(cnt), x); if(summ%cnt==0, scnt++; print(scnt, "  ", cnt) ); cnt++; n=nextprime(n+1) ); } \\note MUST increase precision to 10000+ digits \\Bill McEachen, Feb 04 2014 (PARI) P=1; S=n=0; forprime(p=2, 1e4, S+=P*=p; if(S%n++==0, print1(n", "))) \\ Charles R Greathouse IV, Feb 05 2014 (PARI) is(n)=my(q=prime(n), P=Mod(1, n), S); forprime(p=2, q, S+=P*=p); !S \\ Charles R Greathouse IV, Feb 05 2014 (Python) from itertools import accumulate, count, islice from operator import mul from sympy import prime def A225841_gen(): return (i+1 for i, m in enumerate(accumulate(accumulate((prime(n) for n in count(1)), mul))) if m % (i+1) == 0) A225841_list = list(islice(A225841_gen(), 6)) # Chai Wah Wu, Feb 23 2022 CROSSREFS Cf. A060389, A002110, A045345, A143293, A225727. Sequence in context: A058172 A122808 A294225 * A203509 A009562 A045647 Adjacent sequences:  A225838 A225839 A225840 * A225842 A225843 A225844 KEYWORD nonn,hard,more AUTHOR Alex Ratushnyak, May 21 2013 STATUS approved

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Last modified May 23 00:47 EDT 2022. Contains 353959 sequences. (Running on oeis4.)