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A242776 Primes p such that 2^p + p^2 is not squarefree.

%I A242776 #38 Jun 14 2022 08:51:43
%S A242776 2,11,13,29,31,47,67,83,101,103,137,139,157,173,191,193,211,227,229,
%T A242776 263,281,283,317,337,353,373,389,397,409,421,443,461,463,479,499,569,
%U A242776 571,587,607,641,643,659,661,677,719,733,751,769
%N A242776 Primes p such that 2^p + p^2 is not squarefree.
%C A242776 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
%C A242776 Additional terms: 823, 839, 857, 859, 877, 911, 929, 947, 953, 967, 983. - _Kevin P. Thompson_, Jun 13 2022
%H A242776 Kevin P. Thompson, <a href="/A242776/a242776.txt">Factorizations to support a(n) for n = 1..47</a>
%F A242776 a(n) < (4 + o(1))n log n. - _Charles R Greathouse IV_, May 27 2014
%e A242776 2 is in this sequence because 2 is prime and 2^2 + 2^2 = 8 is divisible by 2^2.
%e A242776 11 is in this sequence because it is prime and 2^11 + 11^2 = 2169 is divisible by 3^2.
%t A242776 Select[Prime[Range[25]], MoebiusMu[2^# + #^2] == 0 &] (* _Alonso del Arte_, May 26 2014 *)
%t A242776 Select[Range[100], PrimeQ[#] && ! SquareFreeQ[2^# + #^2] &] (* _Amiram Eldar_, Dec 24 2020 *)
%o A242776 (Magma) [n: n in [1..265] | IsPrime(n) and not IsSquarefree(2^n + n^2)];
%o A242776 (PARI) s=[]; forprime(p=2, 300, if(!issquarefree(2^p+p^2), s=concat(s, p); print1(p, ", "))); s \\ _Colin Barker_, May 22 2014
%Y A242776 A061238 and A061239 are subsequences.
%Y A242776 Cf. A001580, A005117, A013929.
%K A242776 nonn,more
%O A242776 1,1
%A A242776 _Juri-Stepan Gerasimov_, May 22 2014
%E A242776 a(21)-a(22) from _Charles R Greathouse IV_, May 26 2014
%E A242776 a(23)-a(30) from _Charles R Greathouse IV_, May 27 2014
%E A242776 a(31)-a(34) from _Amiram Eldar_, Dec 24 2020
%E A242776 a(35)-a(47) from _Kevin P. Thompson_, Jan 15 2022
%E A242776 a(48) from _Kevin P. Thompson_, Jun 13 2022