OFFSET
1,1
COMMENTS
This sequence is infinite and its relative density in the sequence of primes is equal to 1 - Product_{p prime} (1-1/(p^2*(p-1))) = 1 - A065414 = 0.302498... (Mirsky, 1949). - Amiram Eldar, Apr 07 2021
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Leon Mirsky, The number of representations of an integer as the sum of a prime and a k-free integer, The American Mathematical Monthly, Vol. 56, No. 1 (1949), pp. 17-19.
MAPLE
filter:= proc(p)
isprime(p) and ormap(t -> t[2]>=3, ifactors(p+1)[2])
end proc:
select(filter, [seq(i, i=3..2000, 2)]); # Robert Israel, Jan 11 2019
MATHEMATICA
f[n_]:=Max[Last/@FactorInteger[n]]; lst={}; Do[p=Prime[n]; If[f[p+1]>=3, AppendTo[lst, p]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 03 2009 *)
PROG
(PARI) ispowerfree(m, p1) = { flag=1; y=component(factor(m), 2); for(i=1, length(y), if(y[i] >= p1, flag=0; break); ); return(flag) }
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) }
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Dec 08 2003
STATUS
approved