

A258896


Divisorial primes p of the form p = 1 + k^2 where k^2 = Product_{dk} d= A007955(k) for some k.


4



2, 37, 101, 197, 677, 5477, 8837, 17957, 21317, 42437, 98597, 106277, 148997, 217157, 401957, 454277, 1196837, 1378277, 1674437, 1705637, 1833317, 1865957, 2390117, 2735717, 3118757, 3147077, 3587237, 3865157, 4104677, 4519877, 4726277, 5410277, 6728837, 7043717
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OFFSET

1,1


COMMENTS

Sequence lists divisorial primes p from A258455 such that p1 = A007955(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 first kind. Divisorial primes of the second kind are in A258897.
With number 3, complement of A258897 with respect to A258455.
All terms > 2 are of the form 4*q^2 + 1 where q = prime (see A052292).
Subsequence of A002496 (primes of the form k^2 + 1), and the corresponding k are a subsequence of A007422.  Michel Marcus, Jul 09 2015


LINKS

Jaroslav Krizek, Table of n, a(n) for n = 1..1000


FORMULA

For n>1; a(n) = 4*(A052291(n))^2 + 1 = A052292(n).


EXAMPLE

Number 101 is in sequence because 100 is the product of divisors of 10; 101  1 = 100 = A007955(sqrt(101  1)).


PROG

(MAGMA) [n: n in [1..10000000]  IsPrime(n) and n1 eq (&*(Divisors(Floor(Sqrt(n1)))))]
(PARI) lista(nn) = {forprime(p=2, nn, if (issquare(pp=(p1)) && (k=sqrtint(pp)) && (d=divisors(k)) && (1+prod(j=1, #d, d[j])==p), print1(p, ", ")); ); } \\ Michel Marcus, Jul 08 2015


CROSSREFS

Cf. A007955, A052292, A258455, A258897, A259199.
Sequence in context: A055031 A041161 A106947 * A262182 A142077 A107182
Adjacent sequences: A258893 A258894 A258895 * A258897 A258898 A258899


KEYWORD

nonn


AUTHOR

Jaroslav Krizek, Jun 20 2015


STATUS

approved



