[seqfan] A018805 optimizations

David Wilson davidwwilson at comcast.net
Thu Jan 19 14:36:37 CET 2017


For a while I've had an idea for optimizations for A018805(n) = { 1 <= x <=
n, 1 <= y <= n, gcd(x, y) = 1 }.
Now that I have a native C++ big integer package, I was able to implement my
ideas.
I was able to compute a(n) for powers of 10 up to 10^12 in a few minutes.  I
got

1e0 1
1e1 63
1e2 6087
1e3 608383
1e4 60794971
1e5 6079301507
1e6 607927104783
1e7 60792712854483
1e8 6079271032731815
1e9 607927102346016827
1e10 60792710185772432731
1e11 6079271018566772422279
1e12 607927101854119608051819






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