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

1,2

Comments

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

Links

Table of n, a(n) for n=1..40.

Formula

T(i,j)=Sum{floor(j*log(p(i))/log(p(h)): h>=1},

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

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

Sequence in context: A120231 A083362 A182847 * A335409 A236341 A293835

Adjacent sequences: A182866 A182867 A182868 * A182870 A182871 A182872

Keyword

nonn,tabl

Author

Clark Kimberling, Dec 09 2010

Extensions

Corrected and extended by Clark Kimberling, Dec 13 2010

Status

approved