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A109314 Numbers n such that prime(n) + n is a prime power (A246547).

%I A109314 #22 Jun 18 2017 02:38:34
%S A109314 3,5,8,9,12,86,230,503,1170,2660,2772,6288,6572,8858,9590,14870,16332,
%T A109314 17708,53132,54540,63890,64908,82830,93068,98132,104726,119298,136502,
%U A109314 152198,177918,187040,234650,241682,253118,263930,278970,376680,412440,456110,469034
%N A109314 Numbers n such that prime(n) + n is a prime power (A246547).
%H A109314 Donovan Johnson, <a href="/A109314/b109314.txt">Table of n, a(n) for n = 1..1000</a>
%F A109314 prime(n) + n = q^k, q is prime and k_Integer >= 2.
%e A109314 2660 is OK because prime(2660) + 2660 = 23909 + 2660 = 26569 = 163^2, 163 is prime.
%p A109314 ispp:= n -> not isprime(n) and nops(numtheory:-factorset(n))=1:
%p A109314 p:= 1: Res:= NULL:
%p A109314 for n from 1 to 10^6 do
%p A109314   p:= nextprime(p);
%p A109314   if ispp(n+p) then Res:= Res, n fi
%p A109314 od:
%p A109314 Res; # _Robert Israel_, Jun 08 2016
%t A109314 lst = {}; fQ[n_] := Block[{pf = FactorInteger[n]}, (2-Length[pf])(pf[[1, 2]]-1) > 0]; Do[ If[ fQ[Prime[n] + n], Print[n]; AppendTo[lst, n]], {n, 456109}]; lst
%o A109314 (Sage) def np(n): return n+nth_prime(n)
%o A109314 [n for n in (1..10000) if not np(n).is_prime() and np(n).is_prime_power()] # _Giuseppe Coppoletta_, Jun 08 2016
%o A109314 (PARI) isok(n) = isprimepower(n+prime(n)) >= 2; \\ _Michel Marcus_, Jun 18 2017
%Y A109314 Cf. A025475 = powers of a prime but not prime, also nonprime n such that sigma(n)*phi(n) > (n-1)2; A107708 = values of q, A107709 = values of k; A107710 = values of prime (A109314(n)).
%Y A109314 Cf. A107605, A246547.
%K A109314 nonn
%O A109314 1,1
%A A109314 _Zak Seidov_ and _Robert G. Wilson v_, Jun 25 2005