A244194 Numbers n such that the difference between the greatest prime divisor of n^2 + 1 and the sum of the other distinct prime divisors is equal to +-1.

268, 411, 606, 657, 1269, 3411, 6981, 8844, 9133, 10509, 28862, 46818, 75163, 81668, 88733, 89238, 107047, 111968, 125793, 143382, 150522, 155317, 179343, 185363, 214547, 222173, 241710, 269051, 305333, 367830, 397387, 492258, 634251, 719379, 724315, 763267

Offset: 1

Author

Michel Lagneau, Jun 22 2014

Keywords

• nonn

Examples

			268 is in the sequence because 268^2 + 1 = 5^2*13^2*17 and 17 - (13 + 5) = 17 - 18 = -1;
411 is in the sequence because 411^2 + 1 = 2 * 13 * 73 * 8 and 89 - (2 + 13 + 73) = 89 - 88 = 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002522.

Programs

Magma

sol:=[]; m:=1; for n in [6..770000] do fp:=PrimeDivisors(n^2+1); big:=Max(fp);  if  #fp ge 2 and Abs(2*big-&+fp) eq 1 then sol[m]:=n; m:=m+1; end if; end for; sol; // Marius A. Burtea, Aug 27 2019

Mathematica

fpdQ[n_]:=Module[{f=Transpose[FactorInteger[n^2+1]][[1]]},Max[f]-Total[Most[f]]==1];gpdQ[n_]:=Module[{g=Transpose[FactorInteger[n^2+1]][[1]]},Max[g]-Total[Most[g]]==-1];Union[Select[Range[2,10^6],fpdQ ],Select[Range[2,10^6],gpdQ ]]
d1Q[n_]:=Module[{c=TakeDrop[FactorInteger[n^2+1][[All,1]],-1]},Abs[ c[[1]] - Total[c[[2]]]]=={1}]; Select[Range[800000],d1Q] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 06 2018 *)