A294208 a(n) = reduced numerator of Sum_{p <= n} Sum_{k=1..floor(log(n)/log(p))} 1/p^k, where p runs over the primes.

0, 0, 1, 5, 13, 77, 77, 599, 1303, 4189, 4189, 48599, 48599, 659507, 659507, 659507, 1364059, 23909723, 23909723, 466536977, 466536977, 466536977, 466536977, 10963143031, 10963143031, 55886560931, 55886560931, 170634254393, 170634254393, 5028706810597

Offset

0,4

Links

Daniel Suteu, Table of n, a(n) for n = 0..300

Formula

a(n) = reduced numerator of Sum_{p <= n} (p^floor(log(n)/log(p)) - 1) / p^floor(log(n)/log(p)) / (p-1), where p runs over the primes.

Prog

(PARI) a(n) = numerator(sum(k=1, primepi(n), sum(j=1, logint(n, prime(k)), 1/prime(k)^j)))
(PARI) a(n) = numerator((sum(k=1, primepi(n), (prime(k)^logint(n, prime(k)) - 1) / prime(k)^logint(n, prime(k)) / (prime(k)-1))))

Crossrefs

The corresponding denominator is A003418.

Sequence in context: A208821 A293259 A064169 * A081525 A027612 A027457

Adjacent sequences: A294205 A294206 A294207 * A294209 A294210 A294211

Keyword

nonn,frac

Author

Daniel Suteu, Oct 24 2017

Status

approved