A140522 -id:A140522 - cp's OEIS frontend

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

Jon E. Schoenfield, Jan 29 2017

nonn

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

			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.

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

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

Cf. A033885.

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

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

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

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

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

A279091 Numbers k for which sigma(k) - 4k exceeds sigma(j) - 4j for all j < k.

Original entry on oeis.org

1, 27720, 50400, 55440, 83160, 110880, 166320, 221760, 277200, 332640, 360360, 443520, 471240, 498960, 554400, 655200, 665280, 720720, 942480, 1053360, 1081080, 1330560, 1413720, 1441440, 1663200, 1801800, 1884960, 2106720, 2162160, 2827440, 2882880, 3326400

Offset: 1

Jon E. Schoenfield, Jan 30 2017

nonn

Does lcm(1..10) = 2520 divide a(n) for all n > 1?

Does lcm(1..11) = 27720 divide a(n) for all n except 1, 3, and 16?

			50400 is in the sequence because sigma(50400) - 4*50400 = 203112 - 201600 = 1512, and no k < 50400 has a value of sigma(k) - 4k this large.

Michel Marcus, Table of n, a(n) for n = 1..77

Cf. A034090, A140522, A279088: with 1, 2 and 3 instead of 4.

lista(nn) = {m = -oo; k = 0; for (n=1, nn, if ((nm = (sigma(n) - 4*n)) > m, k++; print1(n, ", "); m = nm););} \\ Michel Marcus, Nov 02 2017

cp's OEIS Frontend

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

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