OFFSET
2,4
COMMENTS
LINKS
Jonathan Blanchette and Robert Laganière, A Curious Link Between Prime Numbers, the Maundy Cake Problem and Parallel Sorting, arXiv:1910.11749 [cs.DS], 2019.
FORMULA
Let p_k be the k-th prime, where k is the column index, p_k <= n, and n >= 2, and m_k is the multiplicity of p_k occurring in n:
T(n,p_k) = n * 1/(p_1^m_1*p_2^m_2*...*p_k^m_k) * (p_k^m_k-1)/(p_k-1), if p_k divides n;
T(n,p_k) = 0; if p_k does not divide n.
T(2*n,2) = A129527(n); T(2*n+1,2) = 0.
EXAMPLE
First few rows are:
1;
0, 1;
3, 0;
0, 0, 1;
3, 1, 0;
0, 0, 0, 1;
7, 0, 0, 0;
0, 4, 0, 0;
5, 0, 1, 0;
0, 0, 0, 0, 1;
...
Examples (see the p_k formulas)
T(2^3,1) = (2^3-1) / (2-1) = 7
T(3^2,1) = (3^2-1) / (3-1) = 4
T(3*2,2) = (6/(2*3)) * (3^2-1) / (3-1) = 4
T(12,1) = (12/(2^2)) * (2^2-1) / (2-1) = 9
T(12,2) = (12/(2^2*3)) * (3-1) / (3-1) = 1
T(15,2) = (15/3) * (3-1) / (3-1) = 5
T(15,3) = (15/(2^2*3)) * (3-1) / (3-1) = 1
T(2*3*5^2*7,3) = (2*3*5^2*7/(2*3*5^2)) * (5^2-1) / (5-1) = 42
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Jonathan Blanchette, Nov 01 2019
STATUS
approved