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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Number of squarefree derivatives of the divisors of n. LINKS Table of n, a(n) for n=1..92. 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 Adjacent sequences: A348279 A348280 A348281 * A348283 A348284 A348285 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Oct 09 2021 STATUS approved

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Last modified February 26 17:57 EST 2024. Contains 370352 sequences. (Running on oeis4.)