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%I #10 May 30 2023 13:17:39
%S 1,2,4,6,10,14,20,26,36,66,74,84,90,94,110,116,124,126,130,134,146,
%T 150,156,170,180,204,206,210,230,236,260,284,300,306,314,326,340,350,
%U 386,396,406,420,430,436,444,466,470,474,490,556,570,634,636,644,646,654
%N Cubefree numbers n such that n^2 + 1 is prime.
%C Subsequence of A004709.
%C Intersection of A004709 and A005574. - _Robert Israel_, Feb 12 2016
%H K. D. Bajpai, <a href="/A268752/b268752.txt">Table of n, a(n) for n = 1..10000</a>
%e a(5) = 10 = 2 * 5 that is cubefree. 10^2 + 1 = 101 which is a prime.
%e a(6) = 14 = 2 * 7 that is cubefree. 14^2 + 1 = 197 which is a prime.
%p select(t -> isprime(t^2+1) and max(map(f->f[2],ifactors(t)[2]))<=2, [$1..1000]); # _Robert Israel_, Feb 12 2016
%t Select[Range[1000], FreeQ[FactorInteger[#], {_, k_ /; k > 2}] && PrimeQ[#^2 + 1] &]
%t Select[Range[1000],Max[FactorInteger[#][[;;,2]]]<3&&PrimeQ[#^2+1]&] (* _Harvey P. Dale_, May 30 2023 *)
%o (PARI) for(n=1, 1000, f = factor(n)[, 2];if ((#f == 0) || vecmax(f) < 3,if (isprime(n^2+1), print1(n, ", "))));
%Y Cf. A000040, A002496, A004709, A005574, A268697.
%K nonn
%O 1,2
%A _K. D. Bajpai_, Feb 12 2016
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