A294208 - OEIS

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

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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.