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%I #5 Oct 01 2013 17:57:54
%S 3,16,50,145,407,1177,3508,10677,32967,102719,321798,1011538,3186390,
%T 10050746,31730137,100228044,316713624,1001037551,3164497350,
%U 10004755379,31632975601,100021893197,316274794667,1000101078155
%N Numbers of pairs (i, j), i, j > 1, such that i^j <= 10^n.
%C These numbers are related to the divergent series r sum(n^(1/k) = n^1/2 + n^1/3 + ...n^1/r for abs(n) > 0 and r=sqrt(n). k=2
%F a(n) = A089361(10^n) = sum_{p = 2..inf} [floor(10^(n/p)) - 1]. - _David Wasserman_, Sep 14 2005
%e There are 16 perfect powers <= 100: 2^2, 2^3, 3^2, 2^4, 4^2, 5^2, 3^3, 2^5, 6^2, 7^2, 2^6, 4^3, 8^2, 3^4, 9^2, 10^2
%o (PARI) plessn10(n,m) = { for(k=1,n, s=0; z = 10^k; r = floor(sqrt(z)); for(x=m,r, for(y=2,r, p = floor(x^y); if(p<=z,s++) ) ); print1(s",") ) }
%K nonn
%O 1,1
%A _Cino Hilliard_, Dec 27 2003
%E More terms from _David Wasserman_, Sep 14 2005
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