|
%I #18 Jun 03 2017 01:59:55
%S 1,2,6,10,14,26,74,94,130,134,146,170,206,326,386,466,470,634,1094,
%T 1354,1570,1654,1766,1966,2174,2766,3046,3254,3274,3446,4006,4174,
%U 4666,4754,4954,5086,5774,5834,6046,6866,6926,7114,7466,8854,9046,9494,10006,10126
%N Numbers n such that m^2 + n^2/m^2 is prime for every m|n.
%C If n = x*y then x^2 + y^2 is a prime.
%C These n > 1 must be even and squarefree.
%C Conjecture: the set of such n is infinite.
%C The conjecture follows from, e.g., Schinzel's hypothesis H. - _Charles R Greathouse IV_, Jan 28 2014
%H Giovanni Resta, <a href="/A236423/b236423.txt">Table of n, a(n) for n = 1..1000</a>
%t Select[Range[10^4], (d = Divisors[#]^2; And @@ PrimeQ[d + #^2/d]) &]) (* _Giovanni Resta_, Jan 26 2014 *)
%o (PARI) isok(n) = sumdiv(n, d, isprime(d^2 + n^2/d^2)) == numdiv(n); \\ _Michel Marcus_, Jan 25 2014
%o (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
%Y Cf. A080715.
%Y Subsequence of A005574. - _Michel Marcus_, Jun 03 2017
%K nonn
%O 1,2
%A _Thomas Ordowski_, Jan 25 2014
%E More terms from _Michel Marcus_, Jan 25 2014
|
