%I #17 Jun 16 2017 05:25:51

%S 6,16,28,30,32,44,52,54,64,68,70,76,80,104,164,172,174,182,184,186,

%T 196,222,236,238,246,256,260,266,286,292,306,308,310,316,328,344,350,

%U 352,366,374,418,434,436,442,452,474,494,498,508,512,536,548,570,574,582,584,602,628,632,636,642,644,650,654,664,678

%N Numbers n such that n^2 is expressible in just one way as (p+1)(q+1) where p, q are distinct primes.

%H Robert Israel, <a href="/A274848/b274848.txt">Table of n, a(n) for n = 1..10000</a>

%H Zak Seidov, <a href="/A274848/a274848.txt">Table of n, a(n), p, q; n=1..10000</a>

%e 6^2=36=(2+1)*(11+1), 16^2=256=(7+1)(31+1), 28^2=784=(7+1)(97+1).

%p filter:= proc(n) local F, f, count;

%p F:= select(`<`,numtheory:-divisors(n^2),n);

%p count:= 0;

%p for f in F do

%p if isprime(f-1) and isprime(n^2/f-1) then

%p count:=count+1;

%p if count = 2 then return false fi;

%p fi

%p od;

%p count=1

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Jul 08 2016

%t fQ[n_] := Block[{c = 0, p = 2}, While[p < n - 1, If[ PrimeQ[n^2/(p +1) -1], c++]; p = NextPrime@ p]; c == 1]; Select[ Range@1000, fQ] (* _Robert G. Wilson v_, Jul 09 2016 *)

%K nonn

%O 1,1

%A _Zak Seidov_, Jul 08 2016