A062774 Inverse Moebius transform of PrimePi function.

0, 1, 2, 3, 3, 6, 4, 7, 6, 8, 5, 13, 6, 11, 11, 13, 7, 17, 8, 18, 14, 14, 9, 26, 12, 16, 15, 22, 10, 29, 11, 24, 18, 19, 18, 35, 12, 21, 20, 34, 13, 37, 14, 30, 29, 24, 15, 47, 19, 32, 24, 33, 16, 42, 24, 42, 26, 27, 17, 61, 18, 30, 36, 42, 27, 48, 19, 40, 30, 48, 20, 68, 21, 34

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

Cf. A000720, A007444, A007445.

Sequence in context: A337660 A049990 A173739 * A266286 A045892 A160791

Adjacent sequences: A062771 A062772 A062773 * A062775 A062776 A062777

Keyword

nonn

Author

Labos Elemer, Jul 18 2001

Extensions

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

Status

approved