login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..6.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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