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

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

1,1

Comments

A004042(n) factorized with Dario Alpern's ECM.

Extended using factors of 10^(A001913(n)-1)-1, see Kamada link.

Links

Table of n, a(n) for n=1..51.

Dario A. Alpern, Factorization using the Elliptic Curve Method.

Makoto Kamada, Factorizations of 11...11 (Repunit)

Eric Weisstein's World of Mathematics, Cyclic Number

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

Example

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

Crossrefs

Cf. A001913, A087021-A087026.

Sequence in context: A200634 A154177 A010480 * A163409 A312828 A267647

Adjacent sequences: A087018 A087019 A087020 * A087022 A087023 A087024

Keyword

nonn,more,hard

Author

Reinhard Zumkeller, Jul 30 2003

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

Status

approved