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A342323
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Square array read by ascending antidiagonals: T(n,k) = gcd(k, Phi_k(n)), where Phi_k is the k-th cyclotomic polynomial, n >= 0, k >= 1.
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2
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1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 5, 1, 1, 2, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 2, 5, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 2, 3, 2, 1, 1, 1, 2, 3, 1, 1, 1, 1
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OFFSET
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0,5
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COMMENTS
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This is the same table as A342255 but with offset 0. Therefore, the resulting sequences as flattened tables are different. The main entry is A342255.
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LINKS
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FORMULA
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For k > 1, let p be the largest prime factor of k, then T(n,k) = p if p does not divide n and k = p^e*ord(p,n) for some e > 0, where ord(p,n) is the multiplicative order of n modulo p.
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EXAMPLE
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Table begins:
n\k | 1 2 3 4 5 6 7 8 9 10 11 12
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0 | 1 1 1 1 1 1 1 1 1 1 1 1
1 | 1 2 3 2 5 1 7 2 3 1 11 1
2 | 1 1 1 1 1 3 1 1 1 1 1 1
3 | 1 2 1 2 1 1 1 2 1 1 1 1
4 | 1 1 3 1 1 1 1 1 3 5 1 1
5 | 1 2 1 2 1 3 1 2 1 1 1 1
6 | 1 1 1 1 5 1 1 1 1 1 1 1
7 | 1 2 3 2 1 1 1 2 3 1 1 1
8 | 1 1 1 1 1 3 7 1 1 1 1 1
9 | 1 2 1 2 1 1 1 2 1 5 1 1
10 | 1 1 3 1 1 1 1 1 3 1 1 1
11 | 1 2 1 2 5 3 1 2 1 1 1 1
12 | 1 1 1 1 1 1 1 1 1 1 11 1
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MATHEMATICA
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A342323[n_, k_] := GCD[k, Cyclotomic[k, n]];
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PROG
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(PARI) T(n, k) = gcd(k, polcyclo(k, n))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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