%I #15 Jan 09 2019 19:27:28

%S 1,1,1,2,2,2,2,6,3,3,3,3,3,3,3,12,12,12,12,12,12,12,12,12,12,12,12,12,

%T 12,12,12,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,

%U 60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60

%N Denominators of the Riemann prime counting function.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RiemannPrimeCountingFunction.html">Riemann Prime Counting Function</a>

%e 0, 1, 2, 5/2, 7/2, 7/2, 9/2, 29/6, 16/3, 16/3, 19/3, ...

%t Table[Sum[PrimePi[x^(1/k)]/k, {k, Log2[x]}], {x, 100}] // Denominator (* _Eric W. Weisstein_, Jan 09 2019 *)

%o (PARI) a(n) = denominator(sum(k=1, n, if (p=isprimepower(k), 1/p))); \\ _Michel Marcus_, Jan 07 2019

%o (PARI) a(n) = denominator(sum(k=1, logint(n, 2), primepi(sqrtnint(n, k))/k)); \\ _Daniel Suteu_, Jan 07 2019

%Y Cf. A096624.

%K nonn,frac

%O 1,4

%A _Eric W. Weisstein_, Jul 01 2004