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 A306408 a(n) = Sum_{d|n} (-1)^omega(n/d) * d. 0
 1, 1, 2, 1, 4, 2, 6, 1, 5, 4, 10, 2, 12, 6, 8, 1, 16, 5, 18, 4, 12, 10, 22, 2, 19, 12, 14, 6, 28, 8, 30, 1, 20, 16, 24, 5, 36, 18, 24, 4, 40, 12, 42, 10, 20, 22, 46, 2, 41, 19, 32, 12, 52, 14, 40, 6, 36, 28, 58, 8, 60, 30, 30, 1, 48, 20, 66, 16, 44, 24, 70, 5, 72 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS If n is squarefree (A005117), then a(n) = A000010(n) where A000010 is the Euler totient function. LINKS FORMULA a(n) = n * Sum_{d|n} A076479(d)/d. Sum_{k=1..n} a(k) ~ A065469 * n*(n+1)/2. Multiplicative with a(p^e) = p^e - (p^e - 1)/(p-1). PROG (PARI) a(n) = sumdiv(n, d, (-1)^omega(n/d) * d); (PARI) a(n) = my(f=factor(n)); prod(k=1, #f~, f[k, 1]^f[k, 2] - (f[k, 1]^f[k, 2] - 1)/(f[k, 1]-1)); CROSSREFS Cf. A076479, A206369. Sequence in context: A326069 A326068 A318878 * A232626 A322250 A175542 Adjacent sequences:  A306405 A306406 A306407 * A306409 A306410 A306411 KEYWORD nonn,mult AUTHOR Daniel Suteu, Apr 05 2019 STATUS approved

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Last modified June 19 16:48 EDT 2019. Contains 324222 sequences. (Running on oeis4.)