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A182870 Joint-rank array of odd prime powers: p(i+1)^j, i>=1, j>=1, read by antidiagonals.

%I A182870 #7 Mar 30 2012 18:57:12
%S A182870 1,4,2,11,10,3,26,36,18,5,61,127,78,35,6,143,471,381,234,46,7,348,
%T A182870 1867,1987,1760,349,70,8,881,7755,11195,14884,3166,686,111,9,2279
%N A182870 Joint-rank array of odd prime powers:  p(i+1)^j, i>=1, j>=1, read by antidiagonals.
%C A182870 Joint-rank arrays are defined in the first comment at A182801.  A182870 is a permutation of the positive integers.
%e A182870 First, arrange the odd prime powers in rows:
%e A182870 3....9...27....81...
%e A182870 5...25..125...625...
%e A182870 7...49..343...2401...
%e A182870 Then replace each by its ranks when they are all jointly ranked:
%e A182870 1....4...11....26...
%e A182870 2...10...36...127...
%e A182870 3...18...78...381...
%e A182870 5...35..234..1760...
%t A182870 T[i_,j_]:=Sum[Floor[j*Log[Prime[i+1]]/Log[Prime[h]]],{h,2,PrimePi[Prime[i+1]^j]}]; TableForm[Table[T[i,j],{i,1,6},{j,1,6}]]
%Y A182870 A182801, A182869, A182871, A182872, A182942, A182943.
%K A182870 nonn,tabl
%O A182870 1,2
%A A182870 _Clark Kimberling_, Dec 09 2010
%E A182870 Corrected and extended by _Clark Kimberling_, Dec 14 2010