A279088 Numbers k for which sigma(k) - 3k exceeds sigma(j) - 3j for all j < k.

1, 120, 180, 240, 360, 720, 840, 1260, 1440, 1680, 2160, 2520, 3360, 3780, 3960, 4200, 4680, 5040, 7560, 9240, 10080, 12600, 13860, 15120, 18480, 20160, 22680, 25200, 27720, 30240, 32760, 36960, 37800, 40320, 42840, 45360, 50400, 55440, 65520, 75600, 83160

Offset: 1

Author

Jon E. Schoenfield, Jan 29 2017

Keywords

• nonn

Comments

Positions of record lows in A033885. - Robert Israel, Jan 30 2017

Examples

			240 is in the sequence because sigma(240) - 3*240 = 744 - 720 = 24, and no k < 240 has a value of sigma(k) - 3k this large.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..350 (terms 1..125 from Robert Israel)

Crossrefs

Cf. A002093 (d=0), A034090 (d=1), and A140522 (d=2).

Cf. A033885.

Programs

MATLAB

N = 10^6; % to get all terms <= N
V = 1-3*[1:N];
m = V(1);
A(1) = 1;
for n=2:N
  V(n*[1:N/n]) = V(n*[1:N/n]) + n;
  if V(n) > m
    m = V(n);
    A(end+1) = n;
  end
end
A % Robert Israel, Jan 30 2017

Maple

m:= numtheory:-sigma(1) - 3:
count:= 1:
A[1]:= 1:
for n from 2 to 10^6 do
  v:= numtheory:-sigma(n)-3*n;
  if v > m then
     count:= count+1;
     A[count]:= n;
     m:= v;
  fi;
od:
seq(A[i],i=1..count); # Robert Israel, Jan 30 2017

Mathematica

With[{s = Array[DivisorSigma[1, #] - 3 # &, 10^5]}, FirstPosition[s, #][[1]] & /@ Union@ FoldList[Max, s]] (* Michael De Vlieger, Dec 16 2017 *)

PARI

isok(k) = {my(x = sigma(k) - 3*k); for (j=1, k-1, if (sigma(j) - 3*j > x, return (0));); 1;} \\ Michel Marcus, Jan 30 2017

Extensions

Duplicate a(2)-a(43) removed from b-file by Andrew Howroyd, Feb 27 2018