A192770 Numbers k such that k^2 + 1 is divisible by precisely four distinct primes where the sum of the largest and the smallest is equal to the sum of the other two.

948, 1560, 1772, 13236, 36984, 40452, 94536, 100512, 127224, 425808, 757382, 850416, 875784, 1241106, 2102736, 3343164, 4361808, 4530480, 5401464, 8006700, 8645004, 9806604, 10379136, 10829580, 11366424, 11692746, 13960260

Offset: 1

Author

Michel Lagneau, Jul 09 2011

Keywords

• nonn

Examples

			1772 is in the sequence because 1772^2+1 = 5 * 17^2 * 41 * 53 and 5 + 53 = 17 + 41.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..80 (terms below 10^9)

Crossrefs

Cf. A180278, A192771.

Programs

Maple

with(numtheory):for n from 1 to 100000 do:x:=n^2+1:y:=factorset(x):n1:=nops(y):if n1=4 and y[4] + y[1] = y[2]+y[3] then printf ( "%d %d \n",n,x):else fi:od:

Mathematica

seqQ[n_] := Module[{p = FactorInteger[n^2 + 1][[;;,1]]}, Length[p] == 4 && p[[1]] + p[[4]] == p[[2]] + p[[3]]]; Select[Range[10^6], seqQ] (* Amiram Eldar, Jan 15 2020 *)

PARI

is(n)=my(f=factor(n^2+1)[,1]);#f==4&&f[1]+f[4]==f[2]+f[3]
forstep(n=2,1e7,2,if(is(n),print1(n", "))) \\ Charles R Greathouse IV, Jul 11 2011

Extensions

a(10)-a(27) from Charles R Greathouse IV, Jul 11 2011