login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
OFFSET
1,1
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
KEYWORD
nonn
AUTHOR
Zak Seidov, Jul 08 2016
STATUS
approved