A322713 a(n) = numerator of the Riemann prime counting function for 10^n.

0, 16, 428, 445273, 56175529, 991892879, 18296822833013, 3559637526370229, 6427431691337929, 14804074778750628149, 9387415960571046321167, 594663752918349842404169, 200936708396848319452718531, 296345083061712053722716462103, 30189234512048649753828116713823

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 denominators are A322714.

Cf. A000720, A096624.

Programs

PARI

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

Formula

a(n) = A096624(10^n).

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