OFFSET
1,2
COMMENTS
F_n-H_n approaches a constant, 'kappa', conjectured to be equivalent to the difference of B_3-gamma, where B_3 is Mertens' 3rd constant and gamma is Euler's constant.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = numerator[sum(k=1 to n)mu^2(k)/phi(k)] where mu(k) is the Mobius function and phi(k) is Euler's Totient function.
EXAMPLE
Numerators of F_n, e.g., F_1 = (1/1), F_2 = (1/1 + 1/1), ... F_11 = (1/1 + 1/1 + 1/2 + 0 + 1/4 + 1/2 + 1/6 + 0 + 0 + 1/4 + 1/10).
MATHEMATICA
Table[Numerator[Sum[MoebiusMu[k]^2/EulerPhi[k], {k, 1, n}]], {n, 1, 60}]
PROG
(PARI) a(n) = numerator(sum(k=1, n, if (issquarefree(k), 1/eulerphi(k)))); \\ Michel Marcus, Aug 28 2018
CROSSREFS
KEYWORD
frac,nonn
AUTHOR
Dick Boland (abstract(AT)imathination.org), Mar 13 2008, Mar 27 2008
STATUS
approved