OFFSET

1,3

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = Sum_{d|n} pi(d).

G.f.: Sum_{k>=1} pi(k)*x^k/(1 - x^k), where pi(k) is the number of primes <= k (A000720). - Ilya Gutkovskiy, Jan 16 2017

a(n) = Sum_{d|n} omega(d!). - Wesley Ivan Hurt, May 23 2021

EXAMPLE

n = 12: divisors = D(12) = {1,2,3,4,6,12}, pi(D(12)) = {0,1,2,2,3,5} of which the sum is 0+1+2+2+3+5 = 13 so a(12) = 13; a(p(n)) = 0+n = n, for n-th prime p(n).

PROG

(PARI) { for (n=1, 1000, d=divisors(n); write("b062774.txt", n, " ", sum(k=1, length(d), primepi(d[k]))) ) } \\ Harry J. Smith, Aug 10 2009

CROSSREFS

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 18 2001

EXTENSIONS

Offset changed from 0 to 1 by Harry J. Smith, Aug 10 2009

STATUS

approved