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%I #12 Jul 07 2023 14:58:35
%S 6,10,22,38,58,118,122,142,158,202,262,278,362,398,542,698,758,818,
%T 898,922,1042,1138,1142,1262,1282,1322,1478,1502,1642,1762,1858,1982,
%U 2062,2078,2102,2138,2182,2258,2302,2342,2362,2722,2878,2918,2978,2998,3062
%N Semiprimes n such that lpf(n)^spf(n)+1 is also semiprime, where lpf(n) is larger prime factor of n and spf(n) is smaller prime factor of n.
%C There can never be an odd term! Proof. Any odd semiprime is of the form p*q, with 2 < p <= q. Therefore p^q +1 is even. Also p^q+1 is divisible by p+1 and p+1 is greater than 3 and it is even. Therefore p+1 has at least two divisors and we are still left with the factor (p^q+1)/(p+1). QED
%H Dario Alejandro Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>
%e 38=2*19 is a member because 19^2+1=362=2*181.
%t PrimeFactors[n_Integer] := Flatten[ Table[ # [[1]], { # [[2]]}] & /@ FactorInteger[n]]; a = {}; Do[p = PrimeFactors[n]; If[ Length[p] == 2 && Length[ PrimeFactors[ p[[2]]^p[[1]] + 1]] == 2, AppendTo[a, n]], {n, 1000}]; a
%Y Cf. A001358.
%K nonn
%O 1,1
%A _Jason Earls_, Jul 19 2003
%E Edited and extended by _Robert G. Wilson v_, Jul 19 2003
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