A063173 Prime-composite array T(m,n): highest power of the n-th prime that divides the m-th composite, read by antidiagonals.

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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

N. Fernandez, The prime-composite array B(m,n) and the Borve conjectures

Example

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, ...
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: A143714 A004172 A082754 * A120111 A130055 A202452

Adjacent sequences: A063170 A063171 A063172 * A063174 A063175 A063176

Keyword

nonn,tabl

Author

Neil Fernandez, Jul 09 2001

Status

approved