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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..3.

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

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