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 1-7 of 7 results.

A003135 n! is a nontrivial product of factorials. It is conjectured that the list is complete.

Original entry on oeis.org

9, 10, 16
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

A "nontrivial" solution is one in which the largest x! in the product of a(n)! is such that x < a(n)-1. There are no other terms < 10^5. - Jud McCranie, Jun 15 2005

Examples

			9! = 2! * 3! * 3! * 7! and 7 < 9-1, so 9 is in the sequence.
10! = 6! * 7! or 10! = 3! * 5! * 7! and 7 < 10-1, so 10 is in the sequence.
16! = 2! * 5! * 14! and 14 < 16-1, so 16 is in the sequence.

References

  • R. K. Guy, "Unsolved Problems in Number Theory", section B23.

Links

Crossrefs

Cf. A034878, A001013, A058295, A075082, A109095, A109096, A109097, A109098.

A109100 Numbers n such that n! is the product of exactly 2 smaller factorials (greater than 1).

Original entry on oeis.org

10, 16, 24, 48, 96, 144, 192, 288, 384, 720, 768, 864, 1440, 1536, 1728, 3072, 4320, 5184, 6144, 8640, 10368, 12288, 24576, 25920, 31104, 40320, 49152, 51840, 62208, 80640, 86400, 98304
Offset: 1

Views

Author

Jud McCranie, Jun 19 2005

Keywords

Examples

			10! = 3! * 5! * 7! = 6! * 7!, so 10 is in the sequence.

Crossrefs

Cf. A034878, A001013, A003135, A058295, A075082, A109095, A109096, A109097, A109098, A109100, A109101, A109102, A109103.

A109101 Numbers n such that n! is the product of exactly 3 smaller factorials (greater than 1).

Original entry on oeis.org

576, 1152, 2304, 2880, 3456, 4608, 5760, 6912, 9216, 11520, 18432, 20736, 23040, 36864, 41472, 46080, 73728, 92160
Offset: 1

Views

Author

Jud McCranie, Jun 19 2005

Keywords

Crossrefs

Cf. A034878, A001013, A003135, A058295, A075082, A109095, A109096, A109097, A109098, A109099, A109100, A109102, A109103.

A109102 Numbers n such that n! is the product of exactly 4 smaller factorials (greater than 1).

Original entry on oeis.org

13824, 17280, 27648, 34560, 55296, 82944
Offset: 1

Views

Author

Jud McCranie, Jun 19 2005

Keywords

Crossrefs

Cf. A034878, A001013, A003135, A058295, A075082, A109095, A109096, A109097, A109098, A109099, A109100, A109101, A109103.

A109099 Numbers n such that n! can be expressed as the product of smaller factorials > 2.

Original entry on oeis.org

6, 10, 24, 36, 120, 144, 216, 576, 720, 864, 1296, 2880, 3456, 4320, 5040, 5184, 7776, 13824, 14400, 17280, 20736, 25920, 30240, 31104, 40320, 46656, 69120, 82944, 86400
Offset: 1

Views

Author

Jud McCranie, Jun 19 2005

Keywords

Examples

			86400! = 5! * 6! * 86399!, so 86400 is in the sequence.

Crossrefs

Cf. A034878, A001013, A003135, A058295, A075082, A109095, A109096, A109097, A109098.

Extensions

Definition corrected by Jon E. Schoenfield, Jul 02 2010

A109103 Smallest a(n) such that a(n)! can be expressed as the product of smaller factorials, using n distinct factorials greater than 1 (with repetitions allowed).

Original entry on oeis.org

4, 9, 288, 34560
Offset: 2

Views

Author

Jud McCranie, Jun 19 2005

Keywords

Examples

			34560! = 2! * 3! * 4! * 5! * 34559!, using five different factorials, so a(5)=34560.

Crossrefs

Cf. A034878, A001013, A003135, A058295, A075082, A109095, A109096, A109097, A109098, A109099, A109100, A109101, A109102.

A109104 Numbers n such that n! can be expressed as the product of the factorials of prime numbers, repetitions allowed.

Original entry on oeis.org

4, 6, 8, 9, 10, 12, 24, 32, 48, 72, 128, 192, 240, 384, 432, 480, 720, 864, 1152, 1440, 2592, 2880, 5040, 6144, 6912, 8192, 10080, 11520, 15360, 15552, 23040, 25920, 27648, 51840, 62208, 69120, 73728, 86400
Offset: 1

Views

Author

Jud McCranie, Jun 19 2005

Keywords

Examples

			10! = 3! * 5! * 7!, so 10 is in the sequence.

Crossrefs

Cf. A034878, A001013, A003135, A058295, A075082, A109095, A109096, A109097, A109098, A109099, A109100, A109101, A109102, A109103.
Showing 1-7 of 7 results.

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

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