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A089194
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Primes p such that p-1 and p+1 are cube- or higher power-free.
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6
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2, 3, 5, 11, 13, 19, 29, 37, 43, 59, 61, 67, 83, 101, 131, 139, 149, 157, 173, 179, 181, 197, 211, 227, 229, 277, 283, 293, 307, 317, 331, 347, 349, 373, 389, 397, 419, 421, 443, 461, 467, 491, 509, 523, 547, 557, 563, 571, 587, 613, 619, 643, 653, 659, 661
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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EXAMPLE
| 43 is included because 43-1 = 2*3*7 and 43+1 = 2^2*11 are both cube-free.
71 is omitted because the p+1 side, 72 = 2^3*3^2, has a cube factor.
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MATHEMATICA
| f[n_]:=Module[{a=m=0}, Do[If[FactorInteger[n][[m, 2]]>2, a=1], {m, Length[FactorInteger[n]]}]; a]; lst={}; Do[p=Prime[n]; If[f[p-1]==0&&f[p+1]==0, AppendTo[lst, p]], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 15 2009]
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PROG
| (PARI) \input number of iterations n, power p and the number to subtract k. powerfreep2(n, p, d) = { c=0; pc=0; forprime(x=2, n, pc++; if(ispowerfree(x-d, p) && ispowerfree(x+d, 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: A104293 A153002 A042999 * A050229 A053184 A020607
Adjacent sequences: A089191 A089192 A089193 * A089195 A089196 A089197
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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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