login
a(n) = denominator of the Riemann prime counting function for 10^n.
2

%I #10 Mar 13 2019 03:00:13

%S 1,3,15,2520,45045,102960,232792560,5354228880,1115464350,

%T 291136195350,20629078984800,144403552893600,5342931457063200,

%U 856326196254765600,9419588158802421600,3099044504245996706400,4106233968125945635980,16424935872503782543920

%N a(n) = denominator of the Riemann prime counting function for 10^n.

%H Daniel Suteu, <a href="/A322714/b322714.txt">Table of n, a(n) for n = 0..27</a>

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

%F a(n) = A096625(10^n).

%F a(n) = denominator of Sum_{k=1..floor(log_2(10^n))} pi(floor(10^(n/k)))/k, where pi(x) is the prime counting function A000720.

%e 0, 16/3, 428/15, 445273/2520, 56175529/45045, 991892879/102960, 18296822833013/232792560, ...

%o (PARI) a(n) = denominator(sum(k=1, logint(10^n, 2), primepi(sqrtnint(10^n, k))/k));

%Y The corresponding numerators are A322713.

%Y Cf. A000720, A096625.

%K frac,nonn

%O 0,2

%A _Daniel Suteu_, Dec 24 2018