A259021 Numbers k such that k^2 = Product_{d|k} d (= A007955(k)) and simultaneously k^2 + 1 is a divisorial prime (A258455).

1, 6, 10, 14, 26, 74, 94, 134, 146, 206, 314, 326, 386, 466, 634, 674, 1094, 1174, 1294, 1306, 1354, 1366, 1546, 1654, 1766, 1774, 1894, 1966, 2026, 2126, 2174, 2326, 2594, 2654, 2746, 2974, 2986, 3046, 3106, 3134, 3214, 3254, 3274, 3314, 3326, 3334, 3446

Offset

1,2

Comments

First deviation from A259020 is at a(15).

With number 2 complement of A259023 with respect to A118369.

1 together with squarefree semiprimes (A006881) k such that k^2 + 1 is prime. Without the squarefree restriction there will be only one more term, 4. - Amiram Eldar, Sep 25 2022

Links

Danny Rorabaugh, Table of n, a(n) for n = 1..10000

Formula

a(n) = 2*A052291(n) for n > 1. - Amiram Eldar, Sep 25 2022

Example

The number 10 is in sequence because 10^2 = 1*2*5*10 = 100 and simultaneously 101 is prime.

Mathematica

Prepend[2*Select[Prime[Range[2, 300]], PrimeQ[4 #^2 + 1] &], 1] (* Amiram Eldar, Sep 25 2022 *)

Prog

(Magma) [Floor(Sqrt(n-1)): n in [1..10000000] | IsPrime(n) and n-1 eq (&*(Divisors(Floor(Sqrt(n-1)))))]
(Sage) a = [n for n in range(1, 100000) if is_prime(n^2+1) and n^2==prod(list(divisors(n)))] # Danny Rorabaugh, Sep 21 2015

Crossrefs

Union of {1} and (intersection of A005574 and A006881).

Subsequence of A007422, A048943, A259020, A118369.

Cf. A007955, A007422, A048943, A052291, A118369, A258455, A259020, A259023, A258897.

Sequence in context: A119623 A129119 A259020 * A171251 A074980 A363172

Adjacent sequences: A259018 A259019 A259020 * A259022 A259023 A259024

Keyword

nonn

Author

Jaroslav Krizek, Sep 01 2015

Status

approved