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A279088 Numbers k for which sigma(k) - 3k exceeds sigma(j) - 3j for all j < k. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

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

EXAMPLE

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.

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 *)

PROG

(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

(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

CROSSREFS

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

Cf. A033885.

Sequence in context: A023197 A204828 A204830 * A337479 A322377 A247851

Adjacent sequences:  A279085 A279086 A279087 * A279089 A279090 A279091

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Jan 29 2017

EXTENSIONS

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

STATUS

approved

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Last modified April 13 11:24 EDT 2021. Contains 342936 sequences. (Running on oeis4.)