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 1-3 of 3 results.

A369777 Primes that do not divide any 3-Carmichael numbers.

Original entry on oeis.org

2, 1223, 1487, 4007, 4547, 7823, 9839, 10259, 11483, 11807, 11909, 13259, 13967, 14207, 15629, 15803, 16139, 16889, 18287, 19583, 23039, 23879, 24359, 25349, 29339, 30707, 32027, 34883, 36929, 38747, 39113, 39119, 42787, 43223, 44207, 46829, 47189, 49003, 49019, 49157, 53093, 56267, 56909
Offset: 1

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Author

Max Alekseyev, Jan 31 2024

Keywords

Comments

An odd prime p is a term if and only if A290481(A033270(p)) = 0.

Links

Crossrefs

Subsequence of A051663.
Cf. A087788, A290481, A290484

A290484 Odd prime numbers that are factors of only one 3-Carmichael number.

Original entry on oeis.org

3, 11, 59, 197, 389, 467, 479, 503, 563, 719, 839, 887, 1523, 1907, 2087, 2339, 2837, 3167, 3989, 4229, 4259, 4643, 4679, 4787, 4903, 4919, 5417, 5849, 5879, 6299, 7307, 7331, 7577, 7583, 8117
Offset: 1

Views

Author

Amiram Eldar, Aug 03 2017

Keywords

Comments

Beeger proved in 1950 that if p < q < r are primes such that p*q*r is a 3-Carmichael number, then q < 2p^2 and r < p^3. Therefore there is a finite number of 3-Carmichael numbers which divisible by a given prime.
An odd prime p is a term if and only if A290481(A033270(p)) = 1. - Max Alekseyev, Jan 31 2024

Examples

			59 is in the sequence since it is a prime factor of only one 3-Carmichael number: 178837201 = 59 * 1451 * 2089.

References

  • N. G. W. H. Beeger, "On composite numbers n for which a^n == 1 (mod n) for every a prime to n", Scripta Mathematica, Vol. 16 (1950), pp. 133-135.

Links

Crossrefs

Cf. A065091 (Odd primes), A087788 (3-Carmichael numbers), A051663, A290481, A369777.

Extensions

a(1)-a(12) were calculated using Pinch's tables of Carmichael numbers (see links).
a(13)-a(35) from Max Alekseyev, Jan 31 2024

A290482 Odd primes that divide a record number of 3-Carmichael numbers.

Original entry on oeis.org

3, 5, 7, 13, 31, 43, 61, 211, 421, 1171
Offset: 1

Views

Author

Amiram Eldar, Aug 03 2017

Keywords

Comments

The corresponding numbers of 3-Carmichael numbers are: 1, 3, 6, 8, 9, 12, 16, 22, 24, 25, ... They are records of A290481.

Examples

			13 is in the sequence since it is a factor of 8 3-Carmichael numbers, more numbers than for any prime below it: 3 and 11 are factors of a single 3-Carmichael number, 5 is a factor of 3 numbers, and 7 of 6 numbers.

Crossrefs

Cf. A065091 (Odd primes), A087788 (3-Carmichael numbers), A290481.

Extensions

a(10) from Amiram Eldar, Jun 29 2019
Showing 1-3 of 3 results.

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

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