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 1-4 of 4 results.

A129647 Largest order of a permutation of n elements with exactly 2 cycles. Also the largest LCM of a 2-partition of n.

Original entry on oeis.org

0, 1, 2, 3, 6, 5, 12, 15, 20, 21, 30, 35, 42, 45, 56, 63, 72, 77, 90, 99, 110, 117, 132, 143, 156, 165, 182, 195, 210, 221, 240, 255, 272, 285, 306, 323, 342, 357, 380, 399, 420, 437, 462, 483, 506, 525, 552, 575, 600, 621, 650, 675, 702, 725, 756, 783, 812, 837
Offset: 1

Views

Author

Nickolas Reynolds (nickels(AT)gmail.com), Apr 25 2007

Keywords

Comments

a(n) is asymptotic to (n^2)/4.
a(n) = A116921(n)*A116922(n). - Mamuka Jibladze, Aug 22 2019

Examples

			a(26) = 165 because 26 = 11+15 and lcm(11,15) = 165 is maximal.

Links

Crossrefs

Cf. A000793, A129651.
Cf. A116921, A116922.
Maximal LCM of k positive integers with sum n for k = 2..7: this sequence (k=2), A129648 (k=3), A129649 (k=4), A129650 (k=5), A355367 (k=6), A355403 (k=7).

Programs

  • Maple
    a:= n-> `if`(n<2, 0, max(seq(ilcm(i, n-i), i=1..n/2))):
seq(a(n), n=1..60);  # Alois P. Heinz, Feb 16 2013
  • Mathematica
    Join[{0}, Rest[With[{n = 60}, Max[LCM @@@ IntegerPartitions[#, {2}]] & /@ Range[1, n]]]] (* Modified by Philip Turecek, Mar 25 2023 *)
a[n_] := If[n<2, 0, Max[Table[LCM[i, n-i], {i, 1, n/2}]]]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Jul 15 2015, after Alois P. Heinz *)

Formula

G.f.: t^2*(1 + 2*t^3 - 5*t^4 + 8*t^5 - 4*t^6)/((1-t)^2*(1-t^4)). - Mamuka Jibladze, Aug 22 2019

A129648 Largest order of a permutation of n elements with exactly 3 cycles. Also the largest LCM of a 3-partition of n.

Original entry on oeis.org

0, 0, 1, 2, 3, 6, 6, 12, 15, 30, 21, 60, 35, 84, 105, 140, 84, 210, 165, 280, 315, 360, 385, 504, 495, 630, 693, 792, 819, 990, 1001, 1170, 1287, 1430, 1365, 1716, 1683, 2002, 2145, 2310, 2431, 2730, 2805, 3120, 3315, 3570, 3705, 4080, 4199, 4560, 4845, 5168
Offset: 1

Views

Author

Nickolas Reynolds (nickels(AT)gmail.com), Apr 25 2007

Keywords

Comments

a(n) is asymptotic to (n^3)/27.

Examples

			a(9) = 15 because 9 = 5+3+1 and lcm(1,3,5) = 15 is maximal.

Links

Crossrefs

Cf. A000793, A129651.
Maximal LCM of k positive integers with sum n for k = 2..7: A129647 (k=2), this sequence (k=3), A129649 (k=4), A129650 (k=5), A355367 (k=6), A355403 (k=7).

Programs

  • Mathematica
    Max[LCM @@@ Compositions[ #, 3]] & /@ Range[1, n]

A129649 Largest order of a permutation of n elements with exactly 4 cycles. Also the largest LCM of a 4-partition of n.

Original entry on oeis.org

0, 0, 0, 1, 2, 3, 6, 6, 12, 15, 30, 30, 60, 60, 84, 105, 210, 140, 420, 210, 330, 420, 840, 420, 1260, 1155, 1540, 1365, 2520, 1320, 3080, 3465, 3960, 4095, 5544, 5005, 6930, 6435, 8190, 9009, 10296, 8415, 12870, 11781, 13464, 15015, 18018, 17017, 20592, 21879
Offset: 1

Views

Author

Nickolas Reynolds (nickels(AT)gmail.com), Apr 25 2007

Keywords

Comments

a(n) is asymptotic to (n^4)/256.

Examples

			a(18)=140 because 18 = 7+5+2+2 and lcm(2,2,5,7) = 140 is maximal.

Links

Crossrefs

Cf. A000793, A129651.
Maximal LCM of k positive integers with sum n for k = 2..7: A129647 (k=2), A129648 (k=3), this sequence (k=4), A129650 (k=5), A355367 (k=6), A355403 (k=7).

Programs

  • Mathematica
    Max[LCM @@@ Compositions[ #, 4]] & /@ Range[1, n] (* needs Combinatorica *)
Join[{0,0,0},Table[Max[LCM@@#&/@IntegerPartitions[n,{4}]],{n,4,50}]] (* Harvey P. Dale, Feb 25 2012 *)

A129650 Largest order of a permutation of n elements with exactly 5 cycles. Also the largest LCM of a 5-partition of n.

Original entry on oeis.org

0, 0, 0, 0, 1, 2, 3, 6, 6, 12, 15, 30, 30, 60, 60, 84, 105, 210, 210, 420, 420, 420, 420, 840, 840, 1260, 1260, 2310, 1540, 4620, 2520, 5460, 4620, 9240, 5460, 13860, 9240, 16380, 15015, 27720, 13860, 32760, 19635, 40040, 45045, 51480, 32760, 72072, 58905
Offset: 1

Views

Author

Nickolas Reynolds (nickels(AT)gmail.com), Apr 25 2007

Keywords

Comments

a(n) is asymptotic to n^5/3125.

Examples

			a(29)=1540 because 29 = 11+7+5+4+2 and lcm(2,4,5,7,11) = 1540 is maximal.

Links

Crossrefs

Cf. A000793, A129651.
Maximal LCM of k positive integers with sum n for k = 2..7: A129647 (k=2), A129648 (k=3), A129649 (k=4), this sequence (k=5), A355367 (k=6), A355403 (k=7).

Programs

  • Mathematica
    Max[LCM @@@ Compositions[ #, 5]] & /@ Range[1, n]
Showing 1-4 of 4 results.

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