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A259021 Numbers k such that k^2 = Product_{d|k} d (= A007955(k)) and simultaneously k^2 + 1 is a divisorial prime (A258455). 4
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 (list; graph; refs; listen; history; text; internal format)
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
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.
Sequence in context: A119623 A129119 A259020 * A171251 A074980 A363172
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Sep 01 2015
STATUS
approved

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Last modified July 25 02:46 EDT 2024. Contains 374585 sequences. (Running on oeis4.)