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 1-3 of 3 results.

A113467 Least k such that k, k+n and k+2n have the same number of divisors.

Original entry on oeis.org

33, 3, 119, 3, 77, 5, 8, 3, 77, 3, 35, 5, 8, 3, 187, 6, 21, 5, 8, 3, 145, 33, 39, 5, 8, 39, 8, 3, 33, 7, 15, 12, 189, 3, 28, 7, 21, 3, 55, 3, 33, 5, 8, 66, 209, 69, 35, 5, 8, 3, 115, 39, 141, 5, 51, 6, 8, 27, 15, 7, 21, 66, 95, 3, 40, 5, 27, 3, 8, 15, 35, 7, 69, 55, 287, 6, 65, 11, 8, 3, 24
Offset: 1

Views

Author

David Wasserman, Jan 08 2006

Keywords

Comments

Third row of A113465.

Examples

			a(7) = 8 because 8, 15 and 22 each have 4 divisors.

Links

Crossrefs

Cf. A005238, A113458, A113465.

Programs

  • Mathematica
    snd[n_]:=Module[{k=1},While[Length[Union[DivisorSigma[0,{k,k+n,k+2n}]]]>1, k++];k]; Array[snd,90] (* Harvey P. Dale, Aug 20 2017 *)
  • PARI
    a(n) = {k  = 1; until ((numdiv(k) == numdiv(k+n)) && (numdiv(k) == numdiv(k+2*n)), k++); return (k);} \\ Michel Marcus, Jun 16 2013

A113466 Least number that begins an n-term arithmetic progression with common difference 2 in which all terms have the same number of divisors.

Original entry on oeis.org

1, 3, 3, 213, 213, 1383, 3091, 8129, 943607, 943607, 19235031, 21470685, 21470685, 21470685, 21470685
Offset: 1

Views

Author

David Wasserman, Jan 08 2006

Keywords

Comments

Second column of A113465. Next term is > 6368300000.

Examples

			a(4) = 213 because 213, 215, 217 and 219 each have 4 divisors.

Crossrefs

Cf. A113457, A113465.

Programs

  • Mathematica
    Module[{nn=21470695,ds},ds=Table[DivisorSigma[0,n],{n,1,nn,2}];2*Table[ SequencePosition[ds,PadRight[{},k,x_],1],{k,15}][[All,1]]][[All,1]]-1 (* Requires Mathematica version 10 or later *) (* The program will take a long time to run. To generate the first 8 terms of the sequence, change the nn constant to 8200 and the k range from 15 to 8 and the program will run quickly. *) (* Harvey P. Dale, Aug 16 2020 *)

A113468 Least number k such that k, k+n, k+2*n and k+3*n have the same number of divisors.

Original entry on oeis.org

242, 213, 3445, 111, 8718, 5, 2001, 69, 3526, 299, 1074, 5, 2222, 537, 9177, 129, 4114, 5, 8, 598, 7843, 111, 1235, 10, 2984, 303, 3538, 417, 987, 7, 1771, 91, 7659, 57, 9269, 10, 2264, 145, 1197, 219, 1606, 5, 1826, 115, 8897, 203, 618, 5, 8, 159, 2673, 183
Offset: 1

Views

Author

David Wasserman, Jan 08 2006

Keywords

Comments

Fourth row of A113465.

Examples

			a(19) = 8 because 8, 8 + 19 = 27, 8 + 2*19 = 46 and 8 + 3*19 = 65 each have 4 divisors.

Links

Crossrefs

Cf. A113465.

Programs

  • Mathematica
    a[n_] := Module[{k = 1, d}, While[(d = DivisorSigma[0, k]) != DivisorSigma[0, k+n] || DivisorSigma[0, k+2*n] != d || DivisorSigma[0, k+3*n] != d, k++]; k]; Array[a, 60] (* Amiram Eldar, Aug 04 2024 *)
  • PARI
    a(n) = {my(k = 1, d); while((d = numdiv(k)) != numdiv(k+n) || numdiv(k+2*n) != d || numdiv(k+3*n) != d, k++); k;} \\ Amiram Eldar, Aug 04 2024

Extensions

Name corrected by Amiram Eldar, Aug 04 2024
Showing 1-3 of 3 results.

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

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