A382067 -id:A382067 - cp's OEIS frontend

A382083 a(n) is the ratio between A382067(n) and A382067(n+2).

3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 210, 13, 12, 11, 11, 12, 13, 14, 15, 210, 17160, 9, 8, 210, 5, 6, 7, 8, 90, 11, 12, 132, 30240, 6, 7, 8, 9, 72, 7, 7, 8, 8, 8, 9, 72, 7, 7, 72, 10, 11, 12, 132, 10, 9, 336, 6, 7, 8, 9, 9, 9, 10, 90, 8, 7, 7, 72, 10

Offset: 1

Rémy Sigrist, Mar 15 2025

nonn

A382067(n)*A382067(n+1) and A382067(n+1)*A382067(n+2) are factorial numbers, the largest of which, say M, is a multiple of the smallest, say m: a(n) = M/m.

			A382067(7) = 105, A382067(7+2) = 945, so a(7) = 945 / 105 = 9.
A382067(14) = 645120, A382067(14+2) = 3072, so a(14) = 645120 / 3072 = 210.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program

Cf. A382067.

PARI
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a(n) = max(A382067(n), A382067(n+2)) / min(A382067(n), A382067(n+2)).

A382085 a(n) is the unique k such that A382067(n) * A382067(n+1) = k!.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 13, 12, 11, 10, 11, 12, 13, 14, 15, 13, 9, 8, 7, 4, 5, 6, 7, 8, 10, 11, 12, 10, 5, 6, 7, 8, 9, 7, 6, 7, 8, 7, 8, 9, 7, 6, 7, 9, 10, 11, 12, 10, 9, 8, 5, 6, 7, 8, 9, 8, 9, 10, 8, 7, 6, 7, 9, 10, 11, 12, 10, 9, 10

Offset: 1

Rémy Sigrist, Mar 15 2025

nonn

			A382067(15) * A382067(15+1) = 2027025 * 3072 = 13!, so a(15) = 13.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program

Cf. A084558, A382067.

PARI
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a(n) = A084558(A382067(n) * A382067(n+1)).

A382072 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, n*a(n) is a factorial number.

Original entry on oeis.org

1, 3, 2, 6, 24, 4, 720, 15, 80, 12, 3628800, 10, 479001600, 360, 8, 45, 20922789888000, 40, 6402373705728000, 36, 240, 1814400, 1124000727777607680000, 5, 145152, 239500800, 13440, 180, 304888344611713860501504000000, 168, 265252859812191058636308480000000

Offset: 1

Rémy Sigrist, Mar 14 2025

nonn

This sequence is a self-inverse permutation of the positive integers.

			The first terms, alongside n*a(n), are:
  n   a(n)       n*a(n)
  --  ---------  ------
   1          1      1!
   2          3      3!
   3          2      3!
   4          6      4!
   5         24      5!
   6          4      4!
   7        720      7!
   8         15      5!
   9         80      6!
  10         12      5!
  11    3628800     11!
  12         10      5!
  13  479001600     13!
  14        360      7!
  15          8      5!

Index entries for sequences that are permutations of the natural numbers

Cf. A000142, A007672, A382067.

cp's OEIS Frontend

A382083 a(n) is the ratio between A382067(n) and A382067(n+2).

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A382085 a(n) is the unique k such that A382067(n) * A382067(n+1) = k!.

Views

Author

Keywords

Examples

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Crossrefs

Programs

PARI

Formula

A382072 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, n*a(n) is a factorial number.

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Author

Keywords

Comments

Examples

Links

Crossrefs