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%I A330590 #24 Dec 23 2019 06:01:22
%S A330590 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 A330590 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 A330590 2,20,2,8,2,32,2,16,2,24,2,24,2,20,2,8,2,2,72
%N A330590 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 A330590 Peter Kagey, <a href="/A330590/b330590.txt">Table of n, a(n) for n = 2..10012</a> (first 141 rows, flattened)
%F A330590 T(n,k) = A000005(A330541(n,k)).
%F A330590 Conjecture: T(n,1) = 2^A067513(n-1).
%e A330590 Table begins:
%e A330590   n\k| 1   2   3   4   5   6   7   8   9  10  11
%e A330590   ---+-------------------------------------------------
%e A330590    2 | 2;
%e A330590    3 | 4,  2;
%e A330590    4 | 2,  6,  2;
%e A330590    5 | 8,  2,  8,  2;
%e A330590    6 | 2, 12,  2,  8,  2;
%e A330590    7 | 8,  2, 16,  2,  8,  2;
%e A330590    8 | 2, 18,  2, 20,  2,  8,  2;
%e A330590    9 | 8,  2, 24,  2, 20,  2,  8,  2;
%e A330590   10 | 2, 12,  2, 24,  2, 20,  2,  8,  2;
%e A330590   11 | 8,  2, 16,  2, 24,  2, 20,  2,  8,  2;
%e A330590   12 | 2, 12,  2, 20,  2, 24,  2, 20,  2,  8,  2.
%e A330590 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 A330590 Cf. A000005, A330541.
%K A330590 nonn,tabl
%O A330590 2,1
%A A330590 _Peter Kagey_, Dec 18 2019

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