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A134198
Number of distinct sequences {i^k mod n; i >= 0} with k >= 0.
1
1, 2, 3, 4, 5, 3, 7, 5, 8, 5, 11, 4, 13, 7, 5, 8, 17, 8, 19, 6, 7, 11, 23, 5, 22, 13, 21, 8, 29, 5, 31, 13, 11, 17, 13, 8, 37, 19, 13, 7, 41, 7, 43, 12, 14, 23, 47, 8, 44, 22, 17, 14, 53, 21, 21, 9, 19, 29, 59, 6, 61, 31, 8, 22, 13, 11, 67, 18, 23, 13, 71, 9, 73, 37, 22, 20, 31, 13, 79, 8
OFFSET
1,2
LINKS
FORMULA
a(n) = A051903(n) + A002322(n).
EXAMPLE
Let S(k) be the sequence (0^k, 1^k, 2^k, ...) mod 8. S(k) is periodic with period 8 and we find that (1,1,1,1,1,1,1,1,...) = S(0), (0,1,2,3,4,5,6,7,...) = S(1), (0,1,4,1,0,1,4,1,...) = S(2), (0,1,0,3,0,5,0,7,...) = S(3) = S(5) = S(7) = ... and (0,1,0,1,0,1,0,1,...) = S(4) = S(6) = S(8) = ... The first A002322(8) = 3 sequences occur for exactly one value of k. The remaining A051903(8) = 2 sequences occur for an infinite number of k. This gives a(8) = 3+2 = 5.
MATHEMATICA
a[n_] := Max[FactorInteger[n][[;; , 2]]] + CarmichaelLambda[n]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Sep 07 2024 *)
PROG
(PARI) a(n) = if(n == 1, 1, my(f = factor(n)); vecmax(f[, 2]) + lcm(znstar(f)[2])); \\ Amiram Eldar, Sep 07 2024
CROSSREFS
Sequence in context: A346088 A275823 A141295 * A060653 A274690 A081810
KEYWORD
nonn,easy
AUTHOR
David W. Wilson, Oct 13 2007
STATUS
approved