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 A343141 Numbers k such that k*A001414(k)+1 is the square of a prime. 2

%I

%S 8,15,36,48,112,120,280,408,456,760,1036,1584,1785,1800,1936,2856,

%T 3294,3990,4305,4389,14868,18796,19734,21560,29145,30060,30080,30432,

%U 33558,36576,45080,47838,52271,54320,78184,78960,82038,90896,98494,99360,109668,110187,114009,117670,127140,132600

%N Numbers k such that k*A001414(k)+1 is the square of a prime.

%H Robert Israel, <a href="/A343141/b343141.txt">Table of n, a(n) for n = 1..450</a>

%e a(3) = 36 is a term because A001414(36) = 2*2+2*3 = 10 and 36*10+1 = 361 = 19^2 where 19 is prime.

%p sopf:= proc(x) local t; add(t[1]*t[2],t=ifactors(x)[2]) end proc:

%p filter:= proc(n) local x;

%p x:= n*sopf(n)+1;

%p issqr(x) and isprime(sqrt(x))

%p end proc:

%p select(filter, [\$1..10^5]);

%t Select[Range[150000], PrimeQ@ Sqrt[#*Total@ Flatten[ConstantArray @@@ FactorInteger[#]] + 1] &] (* _Michael De Vlieger_, Apr 06 2021 *)

%Y Cf. A001248, A001414.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Apr 06 2021

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Last modified July 31 06:57 EDT 2021. Contains 346369 sequences. (Running on oeis4.)