A226945 - OEIS

A226945

Integer nearest f(10^n), where f(x) = Sum of ( mu(k) * H(k)/k^(3/2) * Integral Log(x^(1/k)) ) for k = 1 to infinity, where H(k) is the harmonic number Sum_{i=1..k} 1/i.

4, 25, 168, 1226, 9585, 78521, 664652, 5761512, 50847348, 455050385, 4118051652, 37607908133, 346065524108, 3204941711340, 29844570436484, 279238341185832, 2623557156537070, 24739954282695698, 234057667295619287, 2220819602542218793

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OFFSET

1,1

COMMENTS

The sequence gives exactly the values of pi(10^n) for n = 1 to 3.

A228724 gives the difference between A006880 and this sequence.

LINKS

David Baugh, Table of n, a(n) for n = 1..100

Chris K. Caldwell, How Many Primes Are There?

Eric Weisstein's World of Mathematics, Prime Counting Function.

Eric Weisstein's World of Mathematics, Prime Number Theorem.

MATHEMATICA