

A063173


Primecomposite array T(m,n): highest power of the nth prime that divides the nth composite, read by antidiagonals.


5



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, 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, 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
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..105.
N. Fernandez, The primecomposite array B(m,n) and the Borve conjectures


EXAMPLE

Let p(n) be the nth prime and c(m) the mth composite. T(1,1)=2 because c(1)=4, p(1)=2 and the highest power of 2 in 4 is 2^2. T(1,2)=0 because c(1)=4, p(2)=3 and the highest power of 3 in 4 is 3^0. T(2,1)=1 because c(2)=6, p(1)=2 and the highest power of 2 in 6 is 2^1. So the sequence starts 2,0,1,...
Array begins
2 0 0 0 0 0 0 ...
1 1 0 0 0 0 0 ...
3 0 0 0 0 0 0 ...
0 2 0 0 0 0 0 ...
1 0 1 0 0 0 0 ...


CROSSREFS

Cf. A000040, A002808, A063174, A063175, A063176.
Sequence in context: A004172 A238942 A082754 * A120111 A130055 A202452
Adjacent sequences: A063170 A063171 A063172 * A063174 A063175 A063176


KEYWORD

nonn,tabl


AUTHOR

Neil Fernandez, Jul 09 2001


STATUS

approved



