A322714 a(n) = denominator of the Riemann prime counting function for 10^n.

1, 3, 15, 2520, 45045, 102960, 232792560, 5354228880, 1115464350, 291136195350, 20629078984800, 144403552893600, 5342931457063200, 856326196254765600, 9419588158802421600, 3099044504245996706400, 4106233968125945635980, 16424935872503782543920

Offset: 0

Author

Daniel Suteu, Dec 24 2018

Keywords

• frac
• nonn

Examples

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

Links

• Daniel Suteu, Table of n, a(n) for n = 0..27
• Eric Weisstein's World of Mathematics, Riemann Prime Counting Function

Crossrefs

The corresponding numerators are A322713.

Cf. A000720, A096625.

Programs

PARI

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

Formula

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

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.