A129649 -id:A129649 - cp's OEIS frontend

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

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

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

a(n) is asymptotic to (n^2)/4.

a(n) = A116921(n)*A116922(n). - Mamuka Jibladze, Aug 22 2019

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

Alois P. Heinz, Table of n, a(n) for n = 1..1000
Index entries for sequences related to lcm's
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).

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).

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

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 *)

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

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

nonn

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

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

Alois P. Heinz, Table of n, a(n) for n = 1..1000
Index entries for sequences related to lcm's

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).

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

A355319 Maximal GCD of four positive integers with sum n.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 3, 4, 1, 3, 1, 5, 3, 2, 1, 6, 5, 2, 3, 7, 1, 6, 1, 8, 3, 2, 7, 9, 1, 2, 3, 10, 1, 7, 1, 11, 9, 2, 1, 12, 7, 10, 3, 13, 1, 9, 11, 14, 3, 2, 1, 15, 1, 2, 9, 16, 13, 11, 1, 17, 3, 14, 1, 18, 1, 2, 15, 19, 11, 13, 1, 20, 9, 2, 1, 21, 17, 2, 3, 22, 1, 18, 13, 23, 3, 2, 19, 24, 1, 14, 11, 25

Offset: 4

Wesley Ivan Hurt, Jun 29 2022

nonn

Cf. A008233, A129649.

Maximal GCD of k positive integers with sum n for k = 2..10: A032742 (k=2,n>=2), A355249 (k=3), this sequence (k=4), A355366 (k=5), A355368 (k=6), A355402 (k=7), A354598 (k=8), A354599 (k=9), A354601 (k=10).

a[n_] := GCD @@@ IntegerPartitions[n, {4}] // Max;
Table[a[n], {n, 4, 100}] (* Jean-François Alcover, Sep 21 2022 *)

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

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

nonn

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

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

Index entries for sequences related to lcm's

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).

Max[LCM @@@ Compositions[ #, 5]] & /@ Range[1, n]

A355367 Maximal LCM of six positive integers with sum n.

Original entry on oeis.org

1, 2, 3, 6, 6, 12, 15, 30, 30, 60, 60, 84, 105, 210, 210, 420, 420, 420, 420, 840, 840, 1260, 1260, 2310, 2310, 4620, 4620, 5460, 5460, 9240, 9240, 13860, 13860, 16380, 16380, 30030, 27720, 60060, 32760, 40040, 60060, 120120, 60060, 180180, 120120, 157080, 120120, 360360

Offset: 6

Wesley Ivan Hurt, Jun 29 2022

nonn

Index entries for sequences related to lcm's

Cf. A008881.

Maximal LCM of k positive integers with sum n for k = 2..7: A129647 (k=2), A129648 (k=3), A129649 (k=4), A129650 (k=5), this sequence (k=6), A355403 (k=7).

Table[Max[LCM@@@IntegerPartitions[n,{6}]],{n,6,60}] (* Harvey P. Dale, Jun 23 2023 *)

a(n) = { my (v=0); forpart(p=n, v=max(v, lcm(Vec(p))),, [6,6]); v } \\ Rémy Sigrist, Jul 01 2022

A355403 Maximal LCM of seven positive integers with sum n.

Original entry on oeis.org

1, 2, 3, 6, 6, 12, 15, 30, 30, 60, 60, 84, 105, 210, 210, 420, 420, 420, 420, 840, 840, 1260, 1260, 2310, 2310, 4620, 4620, 5460, 5460, 9240, 9240, 13860, 13860, 16380, 16380, 30030, 30030, 60060, 60060, 60060, 60060, 120120, 120120, 180180, 180180, 180180, 180180

Offset: 7

Wesley Ivan Hurt, Jun 30 2022

nonn

Index entries for sequences related to lcm's

Cf. A009641, A355368, A355402.

Maximal LCM of k positive integers with sum n for k = 2..7: A129647 (k=2), A129648 (k=3), A129649 (k=4), A129650 (k=5), A355367 (k=6), this sequence (k=7).

A129651 a(n) is the smallest position k at which b_n(i)=k, where b_n(m) is the largest order of a permutation of m elements with exactly n cycles.

Original entry on oeis.org

1, 6, 37, 126, 287, 540, 895

Offset: 1

Nickolas Reynolds (nickels(AT)gmail.com), Apr 25 2007, Apr 26 2007, Apr 27 2007

			a(2)=6 because b_2(6)=5 and b_2(i)<b_2(i+1) for all i>=6. (That is, the largest order of a permutation of i elements with exactly 2 cycles is monotonic increasing starting at i=6.)

Cf. A000793, A129647, A129648, A129649, A129650.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A355319 Maximal GCD of four positive integers with sum n.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A355367 Maximal LCM of six positive integers with sum n.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

A355403 Maximal LCM of seven positive integers with sum n.

Views

Author

Keywords

Links

Crossrefs

A129651 a(n) is the smallest position k at which b_n(i)=k, where b_n(m) is the largest order of a permutation of m elements with exactly n cycles.

Views

Author

Keywords

Examples

Crossrefs