cp's OEIS Frontend

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.

%I A192770 #16 Jan 15 2020 05:51:57
%S A192770 948,1560,1772,13236,36984,40452,94536,100512,127224,425808,757382,
%T A192770 850416,875784,1241106,2102736,3343164,4361808,4530480,5401464,
%U A192770 8006700,8645004,9806604,10379136,10829580,11366424,11692746,13960260
%N 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.
%H A192770 Amiram Eldar, <a href="/A192770/b192770.txt">Table of n, a(n) for n = 1..80</a> (terms below 10^9)
%e A192770 1772 is in the sequence because 1772^2+1 = 5 * 17^2 * 41 * 53 and 5 + 53 = 17 + 41.
%p A192770 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:
%t A192770 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 *)
%o A192770 (PARI) is(n)=my(f=factor(n^2+1)[,1]);#f==4&&f[1]+f[4]==f[2]+f[3]
%o A192770 forstep(n=2,1e7,2,if(is(n),print1(n", "))) \\ _Charles R Greathouse IV_, Jul 11 2011
%Y A192770 Cf. A180278, A192771.
%K A192770 nonn
%O A192770 1,1
%A A192770 _Michel Lagneau_, Jul 09 2011
%E A192770 a(10)-a(27) from _Charles R Greathouse IV_, Jul 11 2011