OFFSET
1,2
COMMENTS
If n = x*y then x^2 + y^2 is a prime.
These n > 1 must be even and squarefree.
Conjecture: the set of such n is infinite.
The conjecture follows from, e.g., Schinzel's hypothesis H. - Charles R Greathouse IV, Jan 28 2014
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..1000
MATHEMATICA
Select[Range[10^4], (d = Divisors[#]^2; And @@ PrimeQ[d + #^2/d]) &]) (* Giovanni Resta, Jan 26 2014 *)
PROG
(PARI) isok(n) = sumdiv(n, d, isprime(d^2 + n^2/d^2)) == numdiv(n); \\ Michel Marcus, Jan 25 2014
(PARI) is(n)=if(n%4!=2, return(n==1)); my(f=factor(n)); if(vecmax(f[, 2])>1, return(0)); fordiv(f, m, if(!isprime(m^2+(n/m)^2), return(0)); if(m^2>n, break)); 1 \\ Charles R Greathouse IV, Jan 28 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Ordowski, Jan 25 2014
EXTENSIONS
More terms from Michel Marcus, Jan 25 2014
STATUS
approved