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A354059
Square array read by ascending antidiagonals: T(n,k) is the number of elements in the multiplicative group of integers modulo n that have order k.
2
1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1, 3, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 3, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
1,32
COMMENTS
Row n and Row n' are the same if and only if (Z/nZ)* = (Z/n'Z)*, where (Z/nZ)* is the multiplicative group of integers modulo n.
For the truncated version see A252911.
LINKS
FORMULA
A327924(n,k) = Sum_{d|k} T(n,k)/phi(d).
EXAMPLE
The 7th, 9th, 14th and 18th rows of A354047 are {1,2,3,2,1,6,1,2,3,2,1,6,...}, so applying the Moebius transform gives {1,1,2,0,0,2,0,0,0,0,0,0,...}.
PROG
(PARI) b(n, k)=my(Z=znstar(n)[2]); prod(i=1, #Z, gcd(k, Z[i]));
T(n, k) = sumdiv(k, d, moebius(k/d)*b(n, d))
CROSSREFS
Moebius transform of A354057 applied to each row.
Cf. A327924.
Sequence in context: A338848 A364045 A166301 * A187081 A369308 A212434
KEYWORD
nonn,tabl
AUTHOR
Jianing Song, May 16 2022
STATUS
approved