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A373217
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Expansion of Sum_{k>=0} x^(7^k) / (1 - x^(7^k)).
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6
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1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2
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OFFSET
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1,7
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LINKS
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FORMULA
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G.f. A(x) satisfies A(x) = x/(1 - x) + A(x^7).
a(7*n+1) = a(7*n+2) = ... = (7*n+6) = 1 and a(7*n+7) = 1 + a(n+1) for n >= 0.
Multiplicative with a(p^e) = e+1 if p = 7, 1 otherwise.
a(n) = -Sum_{d|n} mu(7*d) * tau(n/d).
Dirichlet g.f.: (7^s/(7^s-1)) * zeta(s).
Sum_{k=1..n} a(k) ~ (7/6) * n. (End)
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MATHEMATICA
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a[n_] := 1 + IntegerExponent[n, 7]; Array[a, 100] (* Amiram Eldar, May 29 2024 *)
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PROG
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(PARI) a(n) = valuation(n, 7)+1;
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CROSSREFS
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KEYWORD
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nonn,mult,easy
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AUTHOR
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STATUS
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approved
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