A243609 Numbers n such that the difference between the greatest prime divisor of n^3 + 1 and the sum of the other distinct prime divisors is equal to +-1.

12, 17, 179, 546, 1241, 12520, 19484, 35732, 65933, 76782, 86918, 90035, 94381, 120195, 183677, 209837, 229829, 241951, 288260, 315724, 338712, 344231, 422069, 568346, 597327, 734382, 894504, 1345874, 1635804, 1697093, 2000325, 2043907, 2131745, 2262789, 2492717

Offset: 1

Author

Michel Lagneau, Jun 23 2014

Keywords

• nonn

Examples

			12 is in the sequence because 12^3 + 1 = 1729 = 7 * 13 * 19 and 19 - (13+7) = 19 - 20 = -1;
17 is in the sequence because 17^3 + 1 = 4914 = 2*3^3*7*13 and 13 - (7+3+2) = 13 - 12 = 1.
		

Links

• J. Harrington, L. Jones, A. Lamarche, Representing Integers as the Sum of Two Squares in the Ring Z_n, J. Int. Seq. 17 (2014) # 14.7.4.

Crossrefs

Cf. A001093, A081256, A244194.

Programs

Mathematica

fpdQ[n_]:=Module[{f=Transpose[FactorInteger[n^3+1]][[1]]},Max[f]-Total[Most[f]]==1];gpdQ[n_]:=Module[{g=Transpose[FactorInteger[n^3+1]][[1]]},Max[g]-Total[Most[g]]==-1];Union[Select[Range[2,5*10^6],fpdQ ],Select[Range[2,5*10^6],gpdQ ]]
dgQ[n_]:=Module[{f=FactorInteger[n^3+1][[All,1]],len,a,b},len= Length[ f]-1;{a,b}=TakeDrop[f,len];Abs[Total[a]-b[[1]]]==1]; Select[Range[ 25*10^5],dgQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 03 2019 *)