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A182869 Joint-rank array of prime powers:  p(i)^j, i>=1, j>=1, read by antidiagonals. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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 * A236341 A258145 A175930

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

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Last modified June 28 09:49 EDT 2017. Contains 288813 sequences.