A274848 Numbers n such that n^2 is expressible in just one way as (p+1)(q+1) where p, q are distinct primes.

6, 16, 28, 30, 32, 44, 52, 54, 64, 68, 70, 76, 80, 104, 164, 172, 174, 182, 184, 186, 196, 222, 236, 238, 246, 256, 260, 266, 286, 292, 306, 308, 310, 316, 328, 344, 350, 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

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Zak Seidov, Table of n, a(n), p, q; n=1..10000

Example

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

Maple

filter:= proc(n) local F, f, count;
       F:= select(`<`, numtheory:-divisors(n^2), n);
       count:= 0;
       for f in F do
         if isprime(f-1) and isprime(n^2/f-1) then
           count:=count+1;
           if count = 2 then return false fi;
         fi
       od;
       count=1
end proc:
select(filter, [$1..1000]); # Robert Israel, Jul 08 2016

Mathematica

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 *)

Crossrefs

Sequence in context: A191117 A265389 A320693 * A201020 A088818 A346620

Adjacent sequences: A274845 A274846 A274847 * A274849 A274850 A274851

Keyword

nonn

Author

Zak Seidov, Jul 08 2016

Status

approved