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A089191 Primes p such that p+1 is cubefree. 1

%I

%S 2,3,5,11,13,17,19,29,37,41,43,59,61,67,73,83,89,97,101,109,113,131,

%T 137,139,149,157,163,173,179,181,193,197,211,227,229,233,241,251,257,

%U 277,281,283,293,307,313,317,331,337,347,349,353,373,379,389,397,401,409

%N Primes p such that p+1 is cubefree.

%C 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.

%C 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

%H Robert Israel, <a href="/A089191/b089191.txt">Table of n, a(n) for n = 1..10000</a>

%H Leon Mirsky, <a href="http://www.jstor.org/stable/2305811">The number of representations of an integer as the sum of a prime and a k-free integer</a>, American Mathematial Monthly 56:1 (1949), pp. 17-19.

%e 43 is included because 43+1 = 2^2*11.

%e 71 is omitted because 71+1 = 2^3*3^2.

%p filter:= t -> isprime(t) and max(map(s -> s[2], ifactors(t+1)[2]))<3:

%p select(filter, [2,seq(i,i=3..1000,2)]); # _Robert Israel_, Mar 18 2018

%t Select[Prime[Range[100]],Max[Transpose[FactorInteger[#+1]][[2]]]<3&] (* _Harvey P. Dale_, Jun 06 2013 *)

%o (PARI) is(n) = isprime(n) && vecmax(factor(n+1)[,2]) < 3 \\ _Amiram Eldar_, Feb 16 2021

%Y Cf. A004709, A049097, A065414, A089189.

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Dec 08 2003

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Last modified April 23 06:38 EDT 2021. Contains 343201 sequences. (Running on oeis4.)