A182869 Joint-rank array of prime powers: p(i)^j, i>=1, j>=1, read by antidiagonals.

1, 3, 2, 6, 7, 4, 10, 15, 14, 5, 18, 32, 42, 23, 8, 27, 68, 136, 86, 41, 9, 44, 152, 482, 392, 244, 53, 11, 70, 359, 1880, 2001, 1773, 360, 91, 12, 117, 893, 7771, 11211

Offset: 1

Author

Clark Kimberling, Dec 09 2010

Keywords

• nonn
• tabl

Comments

Joint-rank arrays are defined in the first comment at A182801. A182869 is a permutation of the positive integers.

Examples

			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...
		

Crossrefs

Cf. A000961, A027883, A182801, A182870, A182908.

Programs

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}]]

Formula

T(i,j) = Sum_{h>=1} floor(j*log(p(i))/log(p(h))), where p(i) denotes the i-th prime.

Extensions

Corrected and extended by Clark Kimberling, Dec 13 2010