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

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..48.

Kevin P. Thompson, Factorizations to support a(n) for n = 1..47

Formula

a(n) < (4 + o(1))n log n. - Charles R Greathouse IV, May 27 2014

Example

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.

Mathematica

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 *)

Prog

(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

Crossrefs

A061238 and A061239 are subsequences.

Cf. A001580, A005117, A013929.

Sequence in context: A257329 A063587 A038972 * A373824 A105887 A019407

Adjacent sequences: A242773 A242774 A242775 * A242777 A242778 A242779

Keyword

nonn,more

Author

Juri-Stepan Gerasimov, May 22 2014

Extensions

a(21)-a(22) from Charles R Greathouse IV, May 26 2014

a(23)-a(30) from Charles R Greathouse IV, May 27 2014

a(31)-a(34) from Amiram Eldar, Dec 24 2020

a(35)-a(47) from Kevin P. Thompson, Jan 15 2022

a(48) from Kevin P. Thompson, Jun 13 2022

Status

approved