A244193 Numbers n such that the difference between the greatest prime divisor of n and the sum of the other distinct prime divisors is equal to +-1.

6, 12, 18, 24, 36, 48, 54, 72, 96, 105, 108, 144, 162, 192, 216, 231, 288, 315, 324, 330, 384, 385, 429, 432, 455, 462, 486, 525, 546, 576, 648, 660, 663, 693, 735, 768, 864, 910, 924, 935, 945, 969, 972, 990, 1092, 1105, 1122, 1152, 1235, 1287, 1296, 1309

Offset: 1

Author

Michel Lagneau, Jun 22 2014

Keywords

• nonn

Comments

The sequence A215142 is included in this sequence.

Examples

			105 is in the sequence because 105 = 3*5*7 and 7 - (3 + 5) = 7 - 8 = -1;
231 is in the sequence because 231 = 3 * 7 * 11 and 11 - (3 + 7) = 11 - 10 = 1.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A033845, A215142.

Programs

Maple

filter:= proc(n) local P,pmax;
     P:= numtheory[factorset](n);
     abs(convert(P,`+`)-2*max(P))=1
end proc;
select(filter, [$1..10000]); # Robert Israel, Jun 23 2014

Mathematica

fpdQ[n_]:=Module[{f=Transpose[FactorInteger[n]][[1]]},Max[f]-Total[Most[f]]==1];gpdQ[n_]:=Module[{g=Transpose[FactorInteger[n]][[1]]},Max[g]-Total[Most[g]]==-1];Union[Select[Range[2,3000],fpdQ ],Select[Range[2,3000],gpdQ ]]
dbgQ[n_]:=Module[{fi=FactorInteger[n][[All,1]]},Abs[fi[[-1]]-Total[ Most[ fi]]]==1]; Select[Range[2,1500],dbgQ] (* Harvey P. Dale, Jan 01 2020 *)