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%I #22 Jun 17 2013 10:43:28
%S 4,8,12,16,32,48,64,128,192,256,448,512,768,1024,2048,3072,4096,8192,
%T 12288,16384,28672,32768,49152,65536,131072,196608,262144,524288,
%U 786432,1048576,1835008,2097152,3145728,4194304,4980736,8388608,11534336,12582912
%N Composite numbers n such that p^2 * (p - 1) divides 2(n - p) for every prime p dividing n.
%C On the other hand, no composite numbers are known such that p^2 * (p-1) divides (n-p) for every prime p dividing n.
%t hh[n_] := Module[{aux = FactorInteger[n]}, Union@Table[IntegerQ[2 (n - aux[[i, 1]])/(aux[[i, 1]]^2 * (aux[[i, 1]] - 1))], {i, 1, Length[aux]}] == {True}]; Select[1+Range[50000], !PrimeQ[#] && hh[#] &]
%o (PARI) p=3;forprime(q=5,1e7,for(n=p+1,q-1,f=factor(n)[,1];for(i=1,#f,if(2*(n-f[i])%(f[i]^2*(f[i]-1)),next(2)));print1(n", "));p=q) \\ _Charles R Greathouse IV_, Dec 21 2011
%K nonn
%O 1,1
%A _José María Grau Ribas_, Dec 20 2011
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