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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).

%I A259021 #27 Apr 10 2025 23:23:17
%S A259021 1,6,10,14,26,74,94,134,146,206,314,326,386,466,634,674,1094,1174,
%T A259021 1294,1306,1354,1366,1546,1654,1766,1774,1894,1966,2026,2126,2174,
%U A259021 2326,2594,2654,2746,2974,2986,3046,3106,3134,3214,3254,3274,3314,3326,3334,3446
%N A259021 Numbers k such that k^2 = Product_{d|k} d (= A007955(k)) and simultaneously k^2 + 1 is a divisorial prime (A258455).
%C A259021 First deviation from A259020 is at a(15).
%C A259021 With number 2 complement of A259023 with respect to A118369.
%C A259021 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
%H A259021 Danny Rorabaugh, <a href="/A259021/b259021.txt">Table of n, a(n) for n = 1..10000</a>
%F A259021 a(n) = 2*A052291(n) for n > 1. - _Amiram Eldar_, Sep 25 2022
%e A259021 The number 10 is in sequence because 10^2 = 1*2*5*10 = 100 and simultaneously 101 is prime.
%t A259021 Prepend[2*Select[Prime[Range[2, 300]], PrimeQ[4 #^2 + 1] &], 1] (* _Amiram Eldar_, Sep 25 2022 *)
%o A259021 (Magma) [Floor(Sqrt(n-1)): n in [1..10000000] | IsPrime(n) and n-1 eq (&*(Divisors(Floor(Sqrt(n-1)))))];
%o A259021 (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
%Y A259021 Union of {1} and (intersection of A005574 and A006881).
%Y A259021 Subsequence of A007422, A048943, A259020, A118369.
%Y A259021 Cf. A007955, A007422, A048943, A052291, A118369, A258455, A259020, A259023, A258897.
%K A259021 nonn
%O A259021 1,2
%A A259021 _Jaroslav Krizek_, Sep 01 2015