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A348282
a(n) = Sum_{d|n, d>1} mu(d')^2.
0
0, 1, 1, 1, 1, 3, 1, 1, 2, 3, 1, 3, 1, 2, 2, 1, 1, 5, 1, 3, 3, 3, 1, 3, 2, 3, 2, 2, 1, 6, 1, 1, 3, 3, 2, 5, 1, 3, 2, 3, 1, 6, 1, 3, 4, 2, 1, 3, 2, 4, 2, 3, 1, 5, 2, 2, 3, 3, 1, 6, 1, 3, 5, 1, 2, 7, 1, 3, 3, 5, 1, 5, 1, 3, 4, 3, 2, 6, 1, 3, 2, 3, 1, 6, 3, 2, 2, 3, 1, 10, 2, 2
OFFSET
1,6
COMMENTS
Number of squarefree derivatives of the divisors of n.
FORMULA
a(p) = 1 for primes p, since we have mu(p')^2 = mu(1)^2 = 1.
EXAMPLE
a(6) = 3; the divisors of 6 are 1,2,3,6 and their (arithmetic) derivatives are 0,1,1,5 respectively. 1,1,5 are squarefree, so a(6) = 3.
PROG
(PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
a(n) = sumdiv(n, d, my(x=ad(d)); if (x>0, moebius(ad(d))^2)); \\ Michel Marcus, Oct 10 2021
CROSSREFS
Cf. A003415, A008683 (mu).
Sequence in context: A016464 A245570 A243925 * A030727 A278564 A269973
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Oct 09 2021
STATUS
approved