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%I #26 Sep 08 2022 08:46:12
%S 2,37,101,197,677,5477,8837,17957,21317,42437,98597,106277,148997,
%T 217157,401957,454277,1196837,1378277,1674437,1705637,1833317,1865957,
%U 2390117,2735717,3118757,3147077,3587237,3865157,4104677,4519877,4726277,5410277,6728837,7043717
%N Divisorial primes p of the form p = 1 + k^2 where k^2 = Product_{d|k} d= A007955(k) for some k.
%C Sequence lists divisorial primes p from A258455 such that p-1 = A007955(sqrt(p-1)).
%C If 1 + Product_{d|k} d for some k > 1 is a prime p other than 3, then p-1 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 first kind. Divisorial primes of the second kind are in A258897.
%C With number 3, complement of A258897 with respect to A258455.
%C All terms > 2 are of the form 4*q^2 + 1 where q = prime (see A052292).
%C Subsequence of A002496 (primes of the form k^2 + 1), and the corresponding k are a subsequence of A007422. - _Michel Marcus_, Jul 09 2015
%H Jaroslav Krizek, <a href="/A258896/b258896.txt">Table of n, a(n) for n = 1..1000</a>
%F For n>1; a(n) = 4*(A052291(n))^2 + 1 = A052292(n).
%e Number 101 is in sequence because 100 is the product of divisors of 10; 101 - 1 = 100 = A007955(sqrt(101 - 1)).
%o (Magma) [n: n in [1..10000000] | IsPrime(n) and n-1 eq (&*(Divisors(Floor(Sqrt(n-1)))))]
%o (PARI) lista(nn) = {forprime(p=2, nn, if (issquare(pp=(p-1)) && (k=sqrtint(pp)) && (d=divisors(k)) && (1+prod(j=1, #d, d[j])==p), print1(p, ", ")););} \\ _Michel Marcus_, Jul 08 2015
%Y Cf. A007955, A052292, A258455, A258897, A259199.
%K nonn
%O 1,1
%A _Jaroslav Krizek_, Jun 20 2015
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