

A258897


Divisorial primes p such that p1 = Product_{dk} d for some k < sqrt(p1).


7



331777, 8503057, 9834497, 59969537, 562448657, 916636177, 3208542737, 3782742017, 5006411537, 7676563457, 11574317057, 19565295377, 34188010001, 38167092497, 49632710657, 56712564737, 59553569297, 61505984017, 104086245377, 114733948177
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OFFSET

1,1


COMMENTS

A divisorial prime is a prime p of the form p = 1 + Product_{dk} d for some k (see A007955 and A258455).
Sequence lists divisorial primes p from A258455 such that p1 = A007955(k) for some k < sqrt(p1).
If 1 + Product_{dk} d for some k > 1 is a prime p other than 3, then p1 is a square and p is either of the form k^2 + 1 or h^2 + 1 where h>k. In this sequence are divisorial primes of the second kind. Divisorial primes of the first kind are in A258896.
With numbers 2 and 3, divisorial primes p that are not of the form 4*q^2 + 1 where q = prime.
See A259023  numbers n such that Product_{dn} d is a divisorial prime from this sequence.


LINKS



EXAMPLE

Prime p = 331777 is in sequence because p  1 = 331776 = 576^2 is the product of divisors of 24 and 24 < 576.


PROG

(Magma) Set(Sort([&*(Divisors(n))+1: n in [1..1000]  &*(Divisors(n)) ne n^2 and IsSquare(&*(Divisors(n))) and IsPrime(&*(Divisors(n))+1)]))
(Magma) [n: n in [A258455(n)]  not IsPrime(Floor(Sqrt(n1)) div 2)]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



