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%I #8 Jul 21 2021 09:20:03
%S 2,1,0,3,1,0,0,0,0,0,1,2,0,0,0,2,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,
%T 0,0,4,1,0,0,0,0,0,0,0,1,0,1,1,0,0,0,0,0,0,2,2,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0
%N Prime-composite array T(m,n): highest power of the n-th prime that divides the m-th composite, read by antidiagonals.
%H N. Fernandez, <a href="http://www.borve.org/primeness/pcarray.html">The prime-composite array B(m,n) and the Borve conjectures</a>
%e Let p(n) be the n-th prime and c(m) the m-th composite. T(1,1)=2 because c(1)=4, p(1)=2 and the highest power of 2 in 4 is 2^2. T(2,1)=1 because c(2)=6, p(1)=2 and the highest power of 2 in 6 is 2^1. T(1,2)=0 because c(1)=4, p(2)=3 and the highest power of 3 in 4 is 3^0. So the sequence starts 2, 1, 0, ...
%e Array begins
%e 2 0 0 0 0 0 0 ...
%e 1 1 0 0 0 0 0 ...
%e 3 0 0 0 0 0 0 ...
%e 0 2 0 0 0 0 0 ...
%e 1 0 1 0 0 0 0 ...
%Y Cf. A000040, A002808, A063174, A063175, A063176.
%K nonn,tabl
%O 1,1
%A _Neil Fernandez_, Jul 09 2001
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