OFFSET
1,2
COMMENTS
FORMULA
T(i,j) = Sum_{h>=1} floor(j*log(p(i))/log(p(h))), where p(i) denotes the i-th prime.
EXAMPLE
First, arrange the prime powers in rows:
2....4....8....16....32...
3....9...27....81...243...
5...25..125...625..3125...
Then replace each prime power by its rank when they are all jointly ranked:
1....3....6....10.....18...
2....7...15....32.....68...
4...14...42...136....482...
5...23...86...392...2001...
8...41..244..1773..14901...
MATHEMATICA
T[i_, j_]:=Sum[Floor[j*Log[Prime[i]]/Log[Prime[h]]], {h, 1, PrimePi[Prime[i]^j]}];
TableForm[Table[T[i, j], {i, 1, 6}, {j, 1, 6}]]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Dec 09 2010
EXTENSIONS
Corrected and extended by Clark Kimberling, Dec 13 2010
STATUS
approved