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1, 2, 3, 1, 5, 6, 7, -1, 3, 10, 11, 0, 13, 14, 15, -5, 17, 0, 19, 2, 21, 22, 23, -12, 10, 26, 3, 4, 29, 30, 31, -13, 33, 34, 35, -24, 37, 38, 39, -14, 41, 42, 43, 8, 9, 46, 47, -36, 21, 5, 51, 10, 53, -18, 55, -16, 57, 58, 59, -12, 61, 62, 15, -29, 65, 66, 67, 14, 69, 70, 71, -72, 73, 74, 15, 16, 77, 78, 79, -46, 3, 82, 83, -12, 85
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OFFSET
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1,2
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COMMENTS
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Question: Are a(12) = 0 and a(18) = 0 the only zeros in this sequence?
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ c * n^2, where c = 3/4 - zeta(2)*(1/2 - 1/(4*zeta(3))) = 0.2696411609... . - Amiram Eldar, Feb 22 2024
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MATHEMATICA
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Table[(1/2) If[n == 1, 2, 2 n - DivisorSigma[1, n] + Times @@ (1 + FactorInteger[n][[;; , 1]]) - DivisorSum[n, # &, ! CoprimeQ[#, n/#] &]], {n, 85}] (* Michael De Vlieger, Jun 06 2019 *)
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PROG
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(PARI)
A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
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CROSSREFS
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Cf. A000203, A033879, A034448, A048146, A162296, A325314, A325814, A325973, A325974, A325975, A325977, A325979, A325981.
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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