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
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
KEYWORD
nonn
AUTHOR
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