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 1-8 of 8 results.

A191973 Irregular triangle read by rows: row n consists of n and the positive integers m where m-n divides m*n.

Original entry on oeis.org

1, 2, 1, 2, 3, 4, 6, 2, 3, 4, 6, 12, 2, 3, 4, 5, 6, 8, 12, 20, 4, 5, 6, 10, 30, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 18, 24, 42, 6, 7, 8, 14, 56, 4, 6, 7, 8, 9, 10, 12, 16, 24, 40, 72, 6, 8, 9, 10, 12, 18, 36, 90, 5, 6, 8, 9, 10, 11, 12, 14, 15, 20, 30, 35, 60
Offset: 1

Views

Author

Nathaniel Johnston, Jun 22 2011

Keywords

Comments

The maximum term of the n-th row is n*(n+1). The minimum term of the n-th row seems to be A063428(n) if n>=2. The length of row n is A146564(n) + 1.

Examples

			The triangle begins:
1 2
1 2 3 4  6
2 3 4 6  12
2 3 4 5  6  8  12 20
4 5 6 10 30
2 3 4 5  6  7  8  9  10 12 15 18 24 42
6 7 8 14 56
...

Links

Crossrefs

Cf. A162821 (row 30), A162822 (row 36), A162823 (row 42), A162824 (row 48), A162825 (row 60), A127730.

Programs

  • Maple
    for n from 1 to 10 do for m from 1 to n*(n+1) do if(n=m or m*n mod (m-n) = 0)then printf("%d, ",m): fi: od: od:

A162822 Positive numbers k such that 36*k/(36-k) are integers.

Original entry on oeis.org

9, 12, 18, 20, 24, 27, 28, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 44, 45, 48, 52, 54, 60, 63, 72, 84, 90, 108, 117, 144, 180, 198, 252, 360, 468, 684, 1332
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 13 2009

Keywords

Comments

The number k=36 is explicitly included, treating the result of division through zero as an integer.
Row 36 of A191973.

Crossrefs

Cf. A162688, A162689, A162690, A162691, A162692, A162693, A162694, A162817, A162818, A162819, A162820, A162821, A191973.

Programs

  • Maple
    for m from 1 to 1332 do if(m=36 or m*36 mod (m-36) = 0)then printf("%d, ", m): fi: od: # Nathaniel Johnston, Jun 22 2011
  • Mathematica
    f[a_,b_]:=(a*b)/(a-b); a=36;lst={};Do[If[f[a,n]==IntegerPart[f[a,n]], AppendTo[lst,n]],{n,9!}];lst
Sort[Join[{36},Select[Range[1500],IntegerQ[(36#)/(36-#)]&]]]  (* Harvey P. Dale, Mar 23 2011 *)

Extensions

Keywords fini,full added by R. J. Mathar, Jul 31 2009

A162823 Positive numbers k such that 42*k/(42-k) are integers.

Original entry on oeis.org

6, 14, 21, 24, 28, 30, 33, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 51, 54, 56, 60, 63, 70, 78, 84, 91, 105, 126, 140, 168, 189, 238, 294, 336, 483, 630, 924, 1806
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 13 2009

Keywords

Comments

The number k=42 is explicitly included, treating the result of division through zero as an integer.
Row 42 of A191973.

Crossrefs

Cf. A162688, A162689, A162690, A162691, A162692, A162693, A162694, A162817, A162818, A162819, A162820, A162821, A162822, A191973.

Programs

  • Maple
    for m from 1 to 1806 do if(m=42 or m*42 mod (m-42) = 0)then printf("%d, ", m): fi: od: # Nathaniel Johnston, Jun 22 2011
  • Mathematica
    f[a_,b_]:=(a*b)/(a-b); a=42;lst={};Do[If[f[a,n]==IntegerPart[f[a,n]], AppendTo[lst,n]],{n,9!}];lst
Join[{42},Select[Range[2000],IntegerQ[(42#)/(42-#)]&]]//Quiet//Sort (* Harvey P. Dale, Mar 14 2020 *)

Extensions

Keywords fini,full added by R. J. Mathar, Jul 31 2009

A162824 Positive numbers k such that 48*k/(48-k) are integers.

Original entry on oeis.org

12, 16, 24, 30, 32, 36, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 56, 57, 60, 64, 66, 72, 80, 84, 96, 112, 120, 144, 176, 192, 240, 304, 336, 432, 624, 816, 1200, 2352
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 13 2009

Keywords

Comments

The number k=48 is explicitly included.
Row 48 of A191973.

Crossrefs

Cf. A162688, A162689, A162690, A162691, A162692, A162693, A162694, A162817, A162818, A162819, A162820, A162821, A162822, A162823, A191973.

Programs

  • Maple
    for m from 1 to 2352 do if(m=48 or m*48 mod (m-48) = 0)then printf("%d, ", m): fi: od: # Nathaniel Johnston, Jun 22 2011
  • Mathematica
    f[a_,b_]:=(a*b)/(a-b); a=48;lst={};Do[If[f[a,n]==IntegerPart[f[a,n]], AppendTo[lst,n]],{n,9!}];lst

Extensions

Keywords fini,full added by R. J. Mathar, Jul 31 2009

A162825 Positive numbers k such that 60*k/(60-k) are integers.

Original entry on oeis.org

10, 12, 15, 20, 24, 30, 35, 36, 40, 42, 44, 45, 48, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 72, 75, 76, 78, 80, 84, 85, 90, 96, 100, 105, 108, 110, 120, 132, 135, 140, 150, 160, 180, 204, 210, 240, 260, 285, 300, 360, 420
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 13 2009

Keywords

Comments

The number k=60 is explicitly included. The last entry in the sequence is a(68) = 3660.
Row 60 of A191973.

Links

Crossrefs

Cf. A162688, A162689, A162690, A162691, A162692, A162693, A162694, A162817, A162818, A162819, A162820, A162821, A162822, A162823, A162824, A191973.

Programs

  • Maple
    for n from 1 to 3660 do if(n=60 or type(60*n/(60-n),integer))then printf("%d, ",n): fi: od: # Nathaniel Johnston, Jun 22 2011
  • Mathematica
    f[a_,b_]:=(a*b)/(a-b); a=60;lst={};Do[If[f[a,n]==IntegerPart[f[a,n]], AppendTo[lst,n]],{n,9!}];lst
Select[Range[500],If[#==60,True,IntegerQ[(60#)/(60-#)]]&] (* Harvey P. Dale, Sep 26 2023 *)

Extensions

Keyword fini added by R. J. Mathar, Jul 31 2009

A162826 Positive numbers n such that 2*60*n/(60+n) are integers.

Original entry on oeis.org

12, 15, 20, 30, 36, 40, 60, 84, 90, 100, 120, 140, 165, 180, 228, 240, 300, 340, 390, 420, 540, 660, 740, 840, 1140, 1380, 1740, 2340, 3540, 7140
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 13 2009

Keywords

Crossrefs

Cf. A162688, A162689, A162690, A162691, A162692, A162693, A162694, A162817, A162818, A162819, A162820, A162821, A162822, A162823, A162824, A162825

Programs

  • Mathematica
    f[a_,b_]:=(a*b)/(a+b)*2; a=60;lst={};Do[If[f[a,n]==IntegerPart[f[a,n]], AppendTo[lst,n]],{n,9!}];lst
Select[Range[8000],IntegerQ[(120#)/(60+#)]&] (* Harvey P. Dale, Mar 19 2019 *)

Extensions

Sign in definition flipped by R. J. Mathar, Jul 31 2009

A162828 Positive numbers n such that 2*90*n/(90+n) are integers.

Original entry on oeis.org

10, 18, 30, 45, 60, 72, 90, 110, 126, 135, 180, 210, 234, 270, 315, 360, 450, 510, 558, 585, 720, 810, 990, 1260, 1530, 1710, 1935, 2610, 3150, 3960, 5310, 8010, 16110
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 13 2009

Keywords

Crossrefs

Cf. A162688, A162689, A162690, A162691, A162692, A162693, A162694, A162817, A162818, A162819, A162820, A162821, A162822, A162823, A162824, A162825, A162826

Programs

  • Mathematica
    f[a_,b_]:=(a*b)/(a+b)*2; a=90;lst={};Do[If[f[a,n]==IntegerPart[f[a,n]], AppendTo[lst,n]],{n,9!}];lst
Select[Range[17000],IntegerQ[180 #/(#+90)]&] (* Harvey P. Dale, Sep 22 2011 *)

Extensions

Sign in definition flipped by R. J. Mathar, Jul 31 2009

A162829 Positive numbers n such that 2*120*n/(120+n) are integers.

Original entry on oeis.org

8, 24, 30, 40, 60, 72, 80, 105, 120, 168, 180, 200, 240, 264, 280, 330, 360, 456, 480, 520, 600, 680, 780, 840, 1032, 1080, 1320, 1480, 1680, 1800, 2280, 2760, 3080, 3480, 4680, 5640, 7080, 9480, 14280, 28680
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 13 2009

Keywords

Crossrefs

Cf. A162688, A162689, A162690, A162691, A162692, A162693, A162694, A162817, A162818, A162819, A162820, A162821, A162822, A162823, A162824, A162825, A162826, A162828

Programs

  • Mathematica
    f[a_,b_]:=(a*b)/(a+b)*2; a=120;lst={};Do[If[f[a,n]==IntegerPart[f[a,n]], AppendTo[lst,n]],{n,9!}];lst
Select[Range[30000],IntegerQ[240 #/(120+#)]&] (* Harvey P. Dale, Apr 09 2014 *)

Extensions

Sign in definition flipped by R. J. Mathar, Jul 31 2009
Showing 1-8 of 8 results.

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