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Ranks of primes when all odd prime powers p^j, for j>=1, are jointly ranked.
2

%I #5 Mar 30 2012 18:57:12

%S 1,2,3,5,6,7,8,9,12,13,14,15,16,17,19,20,21,22,23,24,25,27,28,29,30,

%T 31,32,33,34,37,38,39,40,41,42,43,44,45,47,48,49,50,51,52,53,54,55,56,

%U 57,58,59,60,62,63,64,65,66,67,68,69,71,72,73,74,75,76,77,79,80,81,82,84,85,86,87,88,89,90,91,92

%N Ranks of primes when all odd prime powers p^j, for j>=1, are jointly ranked.

%C Column 1 of the array A182870. Complement of A182943.

%e 1,2,3,5,6,7,... are the ranks of 3,5,7,11,13,17...

%e in 3,5,7,9,11,13,17,...

%t T[i_,j_]:=Sum[Floor[j*Log[Prime[i+1]]/Log[Prime[h]]],{h,2,PrimePi[Prime[i+1]^j]}]; Table[Flatten[Table[T[i,j],{i,1,80},{j,1,1}]]]

%Y Cf. A182870, A182943.

%K nonn

%O 1,2

%A _Clark Kimberling_, Dec 14 2010