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%I #19 Feb 16 2021 04:10:07
%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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