login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A118370 Divisorial primes: Primes p such that p = prod_{d|n} d + 1 for some n (ordered by n). 4
2, 3, 37, 101, 197, 331777, 677, 8503057, 9834497, 5477, 59969537, 8837, 17957, 21317, 562448657, 916636177, 42437, 3208542737, 3782742017, 5006411537, 7676563457, 98597, 106277, 11574317057, 19565295377, 416806419029812551937 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A118369 for the corresponding n. These are primes in the sequence 1 + A007955. (The suggested name "divisorial prime" is obviously analogous to that of factorial primes (A088332) and primorial primes (A014545).).

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

The prime 37 is a(3) as there exists a number, A118369(3)=6, such that 37 = 6*3*2*1 + 1, where {1,2,3,6} are all the positive divisors of 6.

MATHEMATICA

Reap[For[n = 1, n <= 500, n++, p = Times @@ Divisors[n]; If[PrimeQ[p+1], Sow[p+1]]]][[2, 1]] (* Jean-Fran├žois Alcover, Oct 07 2016 *)

PROG

(PARI) for(n=1, 2500, s=1; fordiv(n, d, s=s*d); if(isprime(s+1), print1(s+1, ", ")))

CROSSREFS

Cf. A118369, A007955.

Cf. A014545, A088332.

Sequence in context: A109748 A062459 A258455 * A189027 A061576 A221055

Adjacent sequences:  A118367 A118368 A118369 * A118371 A118372 A118373

KEYWORD

nonn

AUTHOR

Rick L. Shepherd, Apr 25 2006

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)