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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A180278, A192771.

Sequence in context: A248785 A199924 A215950 * A187627 A170830 A020366

Adjacent sequences: A192767 A192768 A192769 * A192771 A192772 A192773

Keyword

nonn

Author

Michel Lagneau, Jul 09 2011

Extensions

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

Status

approved