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 1-6 of 6 results.

A087021 Number of distinct prime factors of n-th cyclic number.

Original entry on oeis.org

4, 8, 9, 8, 10, 8, 10, 21, 23, 19, 19, 15, 16, 12, 11, 33, 31, 19, 24, 22, 24, 18, 14, 33, 39, 23, 36, 13, 13, 19, 36, 32, 29, 27, 25, 11, 20, 56, 37, 46, 25, 22, 21, 16, 47, 25, 33, 22, 55, 32, 25
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 30 2003

Keywords

Comments

A004042(n) factorized with Dario Alpern's ECM.
Extended using factors of 10^(A001913(n)-1)-1, see Kamada link.

Examples

			A004042(2) = 142857 = 37*13*11*3^3, therefore a(1) =
#{3,11,13,37} = 4.

Links

Crossrefs

Cf. A001913, A087021-A087026.

Formula

a(n) = A001221(A004042(n+1)).
For n>1, let p = A001913(n). If p is a base-10 Wieferich prime, then a(n) = A102347(p-1) + 2; otherwise a(n) = A102347(p-1) + 1. Also, we have A102347(p-1) = A102347((p-1)/2) + A119704((p-1)/2). - Max Alekseyev, Apr 26 2022

Extensions

a(3) corrected, a(12)-a(42) added by Ray Chandler, Nov 16 2011
a(43)-a(51) from Max Alekseyev, May 13 2022

A087020 Greatest prime factor of n-th cyclic number.

Original entry on oeis.org

37, 5882353, 333667, 513239, 121499449, 11111111111111111111111, 154083204930662557781201849, 39526741, 9999999900000001, 59779577156334533866654838281, 119968369144846370226083377, 8396862596258693901610602298557167100076327481
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 30 2003

Keywords

Comments

A004042(n) factorized with Dario Alpern's ECM.
Extended using factors of 10^(A001913(n)-1)-1, see Kamada link.

Examples

			A004042(2) = 142857 = 37*13*11*3^3, therefore a(1) = 37.

Links

Crossrefs

Cf. A001913, A087021, A087022, A087023, A087024, A087025, A087026.

Formula

a(n) = A006530(A004042(n+1)).

Extensions

a(12) from Ray Chandler, Nov 16 2011

A087022 Total number of prime factors of n-th cyclic number.

Original entry on oeis.org

6, 9, 12, 10, 11, 9, 11, 23, 25, 25, 22, 18, 19, 15, 14, 38, 35, 24, 28, 25, 27, 21, 17, 38, 44, 27, 43, 16, 16, 23, 42, 35, 37, 30, 29, 14, 23, 62, 41, 51, 28, 26, 24, 19, 50, 29, 39, 25, 62, 36, 29
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 30 2003

Keywords

Comments

A004042(n) factorized with Dario Alpern's ECM.
Extended using factors of 10^(A001913(n)-1)-1, see Kamada link.

Examples

			A004042(2) = 142857 = 37*13*11*3^3, therefore a(1) = A087021(1)+2 = 6.

Links

Crossrefs

Cf. A001913, A087020-A087026.

Formula

a(n) = A001222(A004042(n+1)).

Extensions

a(3) corrected, a(12)-a(42) added by Ray Chandler, Nov 16 2011
a(43)-a(51) from Max Alekseyev, May 13 2022

A087024 Number of divisors of n-th cyclic number.

Original entry on oeis.org

32, 384, 1280, 576, 1536, 384, 1536, 4194304, 16777216, 3538944, 1769472, 110592, 221184, 13824, 6912, 48318382080, 9663676416, 3538944, 75497472, 14155776, 56623104, 884736, 55296, 57982058496, 3710851743744, 37748736, 695784701952, 27648, 27648, 2654208
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 30 2003

Keywords

Comments

Calculated with Dario Alpern's ECM.
Extended using factors of 10^(A001913(n)-1)-1, see Kamada link.

Links

Crossrefs

Cf. A001913, A087020, A087021, A087022, A087023, A087025, A087026.

Formula

a(n) = A000005(A004042(n+1)).

Extensions

a(12)-a(42) from Ray Chandler, Nov 16 2011

A087025 Sum of divisors of n-th cyclic number.

Original entry on oeis.org

255360, 17205180696931968, 1951532915603927040, 12430490030984319840000, 9956179688423375044684800000, 6080633705911286890368486450696472902951229440, 4809378729404888733987843426081300724182624228548100710400
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 30 2003

Keywords

Comments

Calculated with Dario Alpern's ECM.
Extended using factors of 10^(A001913(n)-1)-1, see Kamada link.

Links

Crossrefs

Cf. A001913, A087020, A087021, A087022, A087023, A087024, A087026.

Formula

a(n) = A000203(A004042(n+1)).

Extensions

a(12)-a(42) from Ray Chandler, Nov 16 2011

A087023 Maximal exponent in prime factorization of n-th cyclic number.

Original entry on oeis.org

3, 2, 4, 2, 2, 2, 2, 3, 3, 5, 2, 2, 2, 2, 2, 4, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 5, 2, 2, 2, 5, 2, 7, 2, 3, 2, 2, 5, 3, 4, 2, 3, 2, 2, 2, 3, 3, 2, 6, 2, 3
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 30 2003

Keywords

Comments

A004042(n) factorized with Dario Alpern's ECM.
Extended using factors of 10^(A001913(n)-1)-1, see Kamada link.

Examples

			A004042(2) = 142857 = 37*13*11*3^3, therefore a(1) = 3.

Links

Crossrefs

Cf. A001913, A087020, A087021, A087022, A087024, A087025, A087026.

Formula

a(n) = A051903(A004042(n+1)).

Extensions

a(12)-a(42) from Ray Chandler, Nov 16 2011
a(43)-a(51) from Max Alekseyev, May 14 2022
Showing 1-6 of 6 results.

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