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

1,1

Links

Table of n, a(n) for n=1..35.

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.

Example

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.

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 *)

Crossrefs

Cf. A001093, A081256, A244194.

Sequence in context: A045699 A155096 A166674 * A082241 A077294 A206421

Adjacent sequences: A243606 A243607 A243608 * A243610 A243611 A243612

Keyword

nonn

Author

Michel Lagneau, Jun 23 2014

Status

approved