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A242776
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Primes p such that 2^p + p^2 is not squarefree.
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2
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2, 11, 13, 29, 31, 47, 67, 83, 101, 103, 137, 139, 157, 173, 191, 193, 211, 227, 229, 263, 281, 283, 317, 337, 353, 373, 389, 397, 409, 421, 443, 461, 463, 479, 499, 569, 571, 587, 607, 641, 643, 659, 661, 677, 719, 733, 751, 769
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OFFSET
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1,1
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COMMENTS
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Sequence is infinite by Dirichlet's theorem: all primes which are 2 or 4 mod 9 are members. - Charles R Greathouse IV, May 27 2014
Additional terms: 823, 839, 857, 859, 877, 911, 929, 947, 953, 967, 983. - Kevin P. Thompson, Jun 13 2022
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LINKS
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FORMULA
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EXAMPLE
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2 is in this sequence because 2 is prime and 2^2 + 2^2 = 8 is divisible by 2^2.
11 is in this sequence because it is prime and 2^11 + 11^2 = 2169 is divisible by 3^2.
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MATHEMATICA
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Select[Prime[Range[25]], MoebiusMu[2^# + #^2] == 0 &] (* Alonso del Arte, May 26 2014 *)
Select[Range[100], PrimeQ[#] && ! SquareFreeQ[2^# + #^2] &] (* Amiram Eldar, Dec 24 2020 *)
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PROG
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(Magma) [n: n in [1..265] | IsPrime(n) and not IsSquarefree(2^n + n^2)];
(PARI) s=[]; forprime(p=2, 300, if(!issquarefree(2^p+p^2), s=concat(s, p); print1(p, ", "))); s \\ Colin Barker, May 22 2014
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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