cp's OEIS Frontend

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.

%I A244193 #13 Jan 01 2020 19:21:09
%S A244193 6,12,18,24,36,48,54,72,96,105,108,144,162,192,216,231,288,315,324,
%T A244193 330,384,385,429,432,455,462,486,525,546,576,648,660,663,693,735,768,
%U A244193 864,910,924,935,945,969,972,990,1092,1105,1122,1152,1235,1287,1296,1309
%N 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.
%C A244193 The sequence A215142 is included in this sequence.
%H A244193 Robert Israel, <a href="/A244193/b244193.txt">Table of n, a(n) for n = 1..10000</a>
%e A244193 105 is in the sequence because 105 = 3*5*7 and 7 - (3 + 5) = 7 - 8 = -1;
%e A244193 231 is in the sequence because 231 = 3 * 7 * 11 and 11 - (3 + 7) = 11 - 10 = 1.
%p A244193 filter:= proc(n) local P,pmax;
%p A244193      P:= numtheory[factorset](n);
%p A244193      abs(convert(P,`+`)-2*max(P))=1
%p A244193 end proc;
%p A244193 select(filter, [$1..10000]); # _Robert Israel_, Jun 23 2014
%t A244193 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 ]]
%t A244193 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 *)
%Y A244193 Cf. A033845, A215142.
%K A244193 nonn
%O A244193 1,1
%A A244193 _Michel Lagneau_, Jun 22 2014