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 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. 1

%I #13 Jan 01 2020 19:21:09

%S 6,12,18,24,36,48,54,72,96,105,108,144,162,192,216,231,288,315,324,

%T 330,384,385,429,432,455,462,486,525,546,576,648,660,663,693,735,768,

%U 864,910,924,935,945,969,972,990,1092,1105,1122,1152,1235,1287,1296,1309

%N 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 The sequence A215142 is included in this sequence.

%H Robert Israel, <a href="/A244193/b244193.txt">Table of n, a(n) for n = 1..10000</a>

%e 105 is in the sequence because 105 = 3*5*7 and 7 - (3 + 5) = 7 - 8 = -1;

%e 231 is in the sequence because 231 = 3 * 7 * 11 and 11 - (3 + 7) = 11 - 10 = 1.

%p filter:= proc(n) local P,pmax;

%p P:= numtheory[factorset](n);

%p abs(convert(P,`+`)-2*max(P))=1

%p end proc;

%p select(filter, [\$1..10000]); # _Robert Israel_, Jun 23 2014

%t 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 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 Cf. A033845, A215142.

%K nonn

%O 1,1

%A _Michel Lagneau_, Jun 22 2014

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Last modified August 11 17:54 EDT 2024. Contains 375073 sequences. (Running on oeis4.)