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PROG
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(PARI) N=10^9; for(n=2, N, if(Mod(binomial(2*n-1, n-1), n)==1 && !ispower(n) && !isprime(n), print1(n, ", "))); \\ Felix Fröhlich, May 11 2014
(PARI) vp(n, p)=my(s); while(n\=p, s+=n); s
is(n)=my(f=factor(n)[, 1], G); if(#f==1, return(0)); for(i=1, #f, if(vp(2*n-1, f[i]) > vp(n, f[i])+vp(n-1, f[i]), return(0))); G=prod(i=1, #f, f[i]^(log(n)\log(f[i]))); prod(i=n+1, 2*n-1, i/gcd(i, G), Mod(1, n))/prod(i=2, n-1, i/gcd(i, G), Mod(1, n))==1
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