OFFSET
1,1
COMMENTS
The ratio of the count of primes p <= n such that p+1 is cubefree to the count of primes <= n converges to 0.69+ slightly higher than the p-1 variety.
More accurately, the density of this sequence within the primes is Product_{p prime} (1-1/(p^2*(p-1))) = 0.697501... (A065414) (Mirsky, 1949). - Amiram Eldar, Feb 16 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, American Mathematial Monthly 56:1 (1949), pp. 17-19.
EXAMPLE
43 is included because 43+1 = 2^2*11.
71 is omitted because 71+1 = 2^3*3^2.
MAPLE
filter:= t -> isprime(t) and max(map(s -> s[2], ifactors(t+1)[2]))<3:
select(filter, [2, seq(i, i=3..1000, 2)]); # Robert Israel, Mar 18 2018
MATHEMATICA
Select[Prime[Range[100]], Max[Transpose[FactorInteger[#+1]][[2]]]<3&] (* Harvey P. Dale, Jun 06 2013 *)
PROG
(PARI) is(n) = isprime(n) && vecmax(factor(n+1)[, 2]) < 3 \\ Amiram Eldar, Feb 16 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Dec 08 2003
STATUS
approved