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%I #31 Jan 03 2019 14:32:22
%S 12,17,179,546,1241,12520,19484,35732,65933,76782,86918,90035,94381,
%T 120195,183677,209837,229829,241951,288260,315724,338712,344231,
%U 422069,568346,597327,734382,894504,1345874,1635804,1697093,2000325,2043907,2131745,2262789,2492717
%N 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.
%H J. Harrington, L. Jones, A. Lamarche, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Jones/jones14.html">Representing Integers as the Sum of Two Squares in the Ring Z_n</a>, J. Int. Seq. 17 (2014) # 14.7.4.
%e 12 is in the sequence because 12^3 + 1 = 1729 = 7 * 13 * 19 and 19 - (13+7) = 19 - 20 = -1;
%e 17 is in the sequence because 17^3 + 1 = 4914 = 2*3^3*7*13 and 13 - (7+3+2) = 13 - 12 = 1.
%t 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 ]]
%t 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 *)
%Y Cf. A001093, A081256, A244194.
%K nonn
%O 1,1
%A _Michel Lagneau_, Jun 23 2014
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