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A062774
Inverse Moebius transform of PrimePi function.
4
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
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