A333974 Eventual period of A007660 modulo n.

1, 3, 4, 3, 7, 12, 5, 3, 8, 21, 6, 12, 15, 15, 28, 3, 31, 24, 23, 21, 20, 6, 13, 12, 28, 15, 24, 15, 46, 84, 7, 3, 12, 93, 35, 24, 20, 69, 60, 21, 25, 60, 44, 6, 56, 39, 14, 12, 30, 84, 124, 15, 84, 24, 42, 15, 92, 138, 11, 84, 117, 21, 40, 3, 105, 12, 121, 93

Offset

1,2

Comments

If n = p^x * q^y * ... for distinct primes p,q,... then a(n) = lcm {a(p^x), a(q^y), ...}. [Corrected by Andrew Howroyd, Nov 06 2025]

Links

Andrew Howroyd, Table of n, a(n) for n = 1..10000

David A. Corneth, PARI program.

Formula

a(n) | a(k*n), k=2,3,...

Example

a(1) is trivially 1.
For n=2 the sequence is 0, {0,1,1}, {0,1,1}, hence a(2) = 3.
For n=3 the sequence is 0, {0,1,1,2}, {0,1,1,2}, hence a(3) = 4.
For n=4 the sequence is 0,0,1,1, {2,3,3}, {2,3,3}, hence a(4) = 3.
For n=5 the sequence is 0, {0,1,1,2,3,2,2}, {0,1,1,2,3,2,2}, hence a(5) = 7.

Prog

(PARI) See Corneth link \\ David A. Corneth, Sep 04 2020

Crossrefs

Sequence in context: A127737 A358125 A299416 * A163108 A350771 A077005

Adjacent sequences: A333971 A333972 A333973 * A333975 A333976 A333977

Keyword

nonn

Author

Isaac Kaufmann, Sep 03 2020

Extensions

More terms from Jinyuan Wang, Sep 04 2020

Status

approved