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%I #20 Feb 09 2024 10:36:22
%S 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,
%T 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,
%U 1,1,1,1,1,1,1,1,11,1,1,2,3,2,1,1,1,2,3,1,1,1,1
%N 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.
%C 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.
%H Jianing Song, <a href="/A342323/b342323.txt">Table of n, a(n) for n = 0..5049</a> (the first 100 antidiagonals)
%F 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.
%e Table begins:
%e n\k | 1 2 3 4 5 6 7 8 9 10 11 12
%e ------------------------------------------
%e 0 | 1 1 1 1 1 1 1 1 1 1 1 1
%e 1 | 1 2 3 2 5 1 7 2 3 1 11 1
%e 2 | 1 1 1 1 1 3 1 1 1 1 1 1
%e 3 | 1 2 1 2 1 1 1 2 1 1 1 1
%e 4 | 1 1 3 1 1 1 1 1 3 5 1 1
%e 5 | 1 2 1 2 1 3 1 2 1 1 1 1
%e 6 | 1 1 1 1 5 1 1 1 1 1 1 1
%e 7 | 1 2 3 2 1 1 1 2 3 1 1 1
%e 8 | 1 1 1 1 1 3 7 1 1 1 1 1
%e 9 | 1 2 1 2 1 1 1 2 1 5 1 1
%e 10 | 1 1 3 1 1 1 1 1 3 1 1 1
%e 11 | 1 2 1 2 5 3 1 2 1 1 1 1
%e 12 | 1 1 1 1 1 1 1 1 1 1 11 1
%t A342323[n_, k_] := GCD[k, Cyclotomic[k, n]];
%t Table[A342323[n-k+1, k], {n, 0, 15}, {k, n+1}] (* _Paolo Xausa_, Feb 09 2024 *)
%o (PARI) T(n,k) = gcd(k, polcyclo(k,n))
%Y Cf. A342255.
%K nonn,easy,tabl
%O 0,5
%A _Jianing Song_, Mar 08 2021
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