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A274848 Numbers n such that n^2 is expressible in just one way as (p+1)(q+1) where p, q are distinct primes. 4
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 (list; graph; refs; listen; history; text; internal format)
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 A032422

Adjacent sequences:  A274845 A274846 A274847 * A274849 A274850 A274851

KEYWORD

nonn

AUTHOR

Zak Seidov, Jul 08 2016

STATUS

approved

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Last modified August 22 11:56 EDT 2019. Contains 326176 sequences. (Running on oeis4.)