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A242933 Numbers n such that k*n/(k+n) is never prime for all k. 0

%I

%S 2,16,28,36,40,50,52,64,66,70,76,78,88,92,96,100,112,116,120,124,126,

%T 130,136,144,148,154,156,160,162,170,172,176,184,186,188,190,196,204,

%U 208,210,216,220,222,232,236,238,244,246,248,250,256,260,266,268,276,280,286

%N Numbers n such that k*n/(k+n) is never prime for all k.

%C If n were an odd number, k*n/(k+n) would never be prime for all k; these are trivial and are not included. See A242932.

%C It is believed that numbers in A016742 (except 4) are members of this sequence.

%e 16*k/(16+k) is an integer for k = 16, 48, 112, and 240. These k-values give the integers 8, 12, 14, and 15, respectively. Since none are prime, 16 is a member of this sequence.

%o (PARI) a(n)=for(k=1,n*(n-1),s=(k*n)/(k+n);if(floor(s)==s,if(ispseudoprime(s),return(k))))

%o n=1;while(n<300,if(a(2*n)==0,print1(2*n,", "));n+=1)

%Y Cf. A242932.

%K nonn

%O 1,1

%A _Derek Orr_, May 27 2014

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Last modified June 12 09:24 EDT 2021. Contains 344946 sequences. (Running on oeis4.)