OFFSET
1,2
COMMENTS
Numerator of sum of reciprocals of squarefree divisors of n.
(6/Pi^2) * A332881(n)/a(n) is the asymptotic density of numbers that are coprime to their digital sum in base n+1 (see A094387 and A339076 for bases 2 and 10). - Amiram Eldar, Nov 24 2022
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..20000
FORMULA
Numerators of coefficients in expansion of Sum_{k>=1} mu(k)^2*x^k/(k*(1 - x^k)).
a(n) = numerator of Sum_{d|n} mu(d)^2/d.
a(n) = numerator of psi(n)/n.
a(p) = p + 1, where p is prime.
From Amiram Eldar, Nov 24 2022: (Start)
Asymptotic means:
EXAMPLE
1, 3/2, 4/3, 3/2, 6/5, 2, 8/7, 3/2, 4/3, 9/5, 12/11, 2, 14/13, 12/7, 8/5, 3/2, 18/17, ...
MAPLE
a:= n-> numer(mul(1+1/i[1], i=ifactors(n)[2])):
seq(a(n), n=1..80); # Alois P. Heinz, Feb 28 2020
MATHEMATICA
Table[If[n == 1, 1, Times @@ (1 + 1/#[[1]] & /@ FactorInteger[n])], {n, 1, 70}] // Numerator
Table[Sum[MoebiusMu[d]^2/d, {d, Divisors[n]}], {n, 1, 70}] // Numerator
PROG
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Ilya Gutkovskiy, Feb 28 2020
STATUS
approved