A049232 Primes p such that p+2 is divisible by a square.

2, 7, 23, 43, 47, 61, 73, 79, 97, 151, 167, 173, 223, 241, 277, 313, 331, 349, 359, 367, 373, 421, 439, 457, 523, 547, 601, 619, 673, 691, 709, 727, 733, 773, 823, 839, 853, 907, 929, 997, 1033, 1051, 1069, 1087, 1123, 1181, 1213, 1223, 1231, 1249, 1303

Offset

1,1

Comments

This sequence is infinite and its relative density in the sequence of the primes is equal to 1 - 2 * Product_{p prime} (1-1/(p*(p-1))) = 1 - 2 * A005596 = 0.252088... - Amiram Eldar, Feb 27 2021

Links

Table of n, a(n) for n=1..51.

Formula

Primes p such that mu(p+2) = 0.

Example

47 is a term since 47+2 = 49 = 7^2 is a square.
523 is a term since 523+2 = 525 = 5^2*21 is divisible by a square.

Mathematica

Select[Prime[Range[100]], ! SquareFreeQ[ # + 2] &] (* Zak Seidov, Oct 28 2008 *)

Prog

(PARI) powerfreep3(n, p, k) = { c=0; pc=0; forprime(x=2, n, pc++; if(ispowerfree(x+k, p)==0, c++; print1(x", "); ) ); print(); print(c", "pc", "c/pc+.0) }
ispowerfree(m, p1) = { flag=1; y=component(factor(m), 2); for(i=1, length(y), if(y[i] >= p1, flag=0; break); ); return(flag) }

Crossrefs

A091880 gives prime indices.

Cf. A005596, A013929, A049229, A049233.

Sequence in context: A045383 A244576 A089176 * A100917 A049552 A049572

Adjacent sequences: A049229 A049230 A049231 * A049233 A049234 A049235

Keyword

nonn

Author

Labos Elemer

Extensions

Corrected by Cino Hilliard and Ray Chandler, Dec 08 2003

Edited by N. J. A. Sloane, Oct 27 2008 at the suggestion of R. J. Mathar

Status

approved