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A089191
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Primes p such that p+1 is cube- or higher power-free.
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0
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| The ratio of the count of primes p <= n such that p+1 is cube-free to the count of primes <= n converges to 0.69+ slightly higher than the p-1 variety.
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EXAMPLE
| 43 is included because 43+1 = 2^2*11. 71 is omitted because 71+1 = 2^3*3^2.
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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) }
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CROSSREFS
| Sequence in context: A042998 A091317 A088254 * A038947 A095315 A140558
Adjacent sequences: A089188 A089189 A089190 * A089192 A089193 A089194
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KEYWORD
| easy,nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Dec 08 2003
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