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%I #24 Dec 23 2019 06:01:22
%S 2,4,2,2,6,2,8,2,8,2,2,12,2,8,2,8,2,16,2,8,2,2,18,2,20,2,8,2,8,2,24,2,
%T 20,2,8,2,2,12,2,24,2,20,2,8,2,8,2,16,2,24,2,20,2,8,2,2,12,2,20,2,24,
%U 2,20,2,8,2,32,2,16,2,24,2,24,2,20,2,8,2,2,72
%N Triangle read by rows: T(n,k) is the number of positive integers m dividing x^n - x^k for all integers x, 0 < k < n.
%H Peter Kagey, <a href="/A330590/b330590.txt">Table of n, a(n) for n = 2..10012</a> (first 141 rows, flattened)
%F T(n,k) = A000005(A330541(n,k)).
%F Conjecture: T(n,1) = 2^A067513(n-1).
%e Table begins:
%e n\k| 1 2 3 4 5 6 7 8 9 10 11
%e ---+-------------------------------------------------
%e 2 | 2;
%e 3 | 4, 2;
%e 4 | 2, 6, 2;
%e 5 | 8, 2, 8, 2;
%e 6 | 2, 12, 2, 8, 2;
%e 7 | 8, 2, 16, 2, 8, 2;
%e 8 | 2, 18, 2, 20, 2, 8, 2;
%e 9 | 8, 2, 24, 2, 20, 2, 8, 2;
%e 10 | 2, 12, 2, 24, 2, 20, 2, 8, 2;
%e 11 | 8, 2, 16, 2, 24, 2, 20, 2, 8, 2;
%e 12 | 2, 12, 2, 20, 2, 24, 2, 20, 2, 8, 2.
%e For n=4 and k=2, the sequence x^4 - x^2 evaluated on the positive (equivalently, negative) integers is 0,12,72,240,600,1260,2352,4032,6480,9900,... and all terms are divisible by the following T(4,2) = 6 positive integers: 1, 2, 3, 4, 6, and 12.
%Y Cf. A000005, A330541.
%K nonn,tabl
%O 2,1
%A _Peter Kagey_, Dec 18 2019
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