cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A033945 Record highs in A033885 (3n - sum of divisors of n).

Original entry on oeis.org

2, 3, 5, 9, 13, 14, 21, 25, 33, 37, 45, 57, 61, 73, 81, 85, 93, 105, 117, 121, 133, 141, 145, 157, 165, 177, 193, 201, 205, 213, 217, 225, 230, 253, 261, 273, 277, 297, 301, 313, 325, 333, 345, 357, 361, 381, 385, 393, 397, 421, 445, 453, 457, 465, 477, 481
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A033885, A033946.

Programs

  • Mathematica
    f[n_] := 3n - DivisorSigma[1, n]; fm = 0; s = {}; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, fm]], {n, 1, 250}]; s (* Amiram Eldar, Aug 28 2019 *)

Extensions

More terms from Asher Auel, May 05 2000

A033946 Values of n corresponding to A033945.

Original entry on oeis.org

1, 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A033885, A033945.

Programs

  • Mathematica
    f[n_] := 3n - DivisorSigma[1, n]; fm = 0; s = {}; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, n]], {n, 1, 263}]; s (* Amiram Eldar, Aug 28 2019 *)

Extensions

More terms from Asher Auel May 05 2000

A037159 Consider the trajectory of n under the iteration of a map which sends x to 3x - sigma(x) if this is >= 0; otherwise the iteration stops. The sequence gives values of n which eventually reach 0.

Original entry on oeis.org

82, 120, 280, 672, 1464, 3048, 4964, 5568, 5688, 7666, 8969, 9176, 9288, 9514, 9616, 9706, 10132, 10186, 10232, 10478, 11496, 11884, 11914, 12232, 12320, 12820, 13248, 13842, 13854, 13866, 14848, 15076, 15098, 15196, 15364, 15586, 15892
Offset: 1

Views

Author

Naohiro Nomoto

Keywords

Comments

A perfect number is a fixed point of this map.

Examples

			82 -> 120 -> 0.

Crossrefs

To see why 1, 16 and 23 are not in the sequence, see A058541, A058542 and A058545.
Cf. A033885, A033945, A033946, A037160.

Programs

Extensions

Better description from Jud McCranie, Dec 24 2000
Definition clarified by Harvey P. Dale, Jul 30 2020

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

Original entry on oeis.org

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

Views

Author

Jon E. Schoenfield, Jan 29 2017

Keywords

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

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

A099738 a(n) = 2*Sum_{k=1..n} (n+1-k) (Sum_{j|k} 1/floor(n/j)).

Original entry on oeis.org

2, 5, 10, 15, 24, 30, 43, 52, 66, 78, 99, 107, 132, 150, 171, 188, 221, 236, 273, 291, 322, 352, 397, 409, 453, 489, 530, 558, 615, 633, 694, 727, 778, 826, 883, 900, 973, 1027, 1088, 1118, 1199, 1229, 1314, 1362, 1419, 1485, 1578, 1598, 1688, 1745, 1826, 1884
Offset: 1

Views

Author

Leroy Quet, Nov 09 2004

Keywords

Comments

Sequence consists entirely of integers.
First differences give A033885.

Programs

  • Mathematica
    f[n_] := 2Sum[(n + 1 - k)*Plus @@ (1/Floor[n/Divisors[k]]), {k, n}]; Table[ f[n], {n, 52}] (* Robert G. Wilson v, Nov 12 2004 *)

Extensions

More terms from Robert G. Wilson v, Nov 12 2004
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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