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%I #37 Jul 04 2017 04:02:47
%S 1,2,5,7,9,10,11,13,15,16,17,19,21,22,23,25,26,27,28,29,31,33,34,35,
%T 36,37,39,40,41,43,45,46,47,49,50,51,52,53,55,57,58,59,61,63,64,65,66,
%U 67,69,70,71,73,75,76,77,78,79,81,82,83,85,86,87,88,89,91,92,93,94,95,96,97,99,100
%N Numbers n such that n - n^2/k^2 is not prime for all k < n.
%C Conjecture: numbers n such that n-1 is not a prime number. - _Vincenzo Librandi_, Jul 16 2016
%C Counterexamples to conjecture: 56, 306, 552, 870, ... are not in the sequence. These are p^2+p where p is prime but p^2+p-1 is not prime. - _Robert Israel_, Jul 04 2017
%H Robert Israel, <a href="/A241884/b241884.txt">Table of n, a(n) for n = 1..10000</a>
%e 56 is not in the sequence because 56 - 56^2/8^2 = 7 is prime for k = 8.
%p filter:= n -> andmap(t -> not isprime(n - t^2), numtheory:-divisors(n)):
%p select(filter, [$1..1000]); # _Robert Israel_, Jul 04 2017
%o (PARI) isOK(n) = fordiv(n, k, if(isprime(n-(n/k)^2), return(0))); 1
%o s=[]; for(n=1, 100, if(isOK(n), s=concat(s, n))); s \\ _Colin Barker_, May 16 2014
%Y Cf. A008864, A036690, A138666 (numbers n such that 2n - n/k is not prime for all k), A242221.
%K nonn
%O 1,2
%A _Ilya Lopatin_ and _Juri-Stepan Gerasimov_, Apr 30 2014
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