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A089191 Primes p such that p+1 is cube- or higher power-free. 1
2, 3, 5, 11, 13, 17, 19, 29, 37, 41, 43, 59, 61, 67, 73, 83, 89, 97, 101, 109, 113, 131, 137, 139, 149, 157, 163, 173, 179, 181, 193, 197, 211, 227, 229, 233, 241, 251, 257, 277, 281, 283, 293, 307, 313, 317, 331, 337, 347, 349, 353, 373, 379, 389, 397, 401, 409 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

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) powerfreep(n, p) = { c=0; pc=0; forprime(x=2, n, pc++; if(ispowerfree(x+1, p), 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

Sequence in context: A042998 A091317 A088254 * A225184 A038947 A095315

Adjacent sequences:  A089188 A089189 A089190 * A089192 A089193 A089194

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, Dec 08 2003

STATUS

approved

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Last modified July 22 14:46 EDT 2019. Contains 325224 sequences. (Running on oeis4.)