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

Author

Reinhard Zumkeller, Jul 30 2003

Keywords

• nonn
• more
• hard

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

• Dario A. Alpern, Factorization using the Elliptic Curve Method.
• Makoto Kamada, Factorizations of 11...11 (Repunit)
• Eric Weisstein's World of Mathematics, Cyclic Number

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