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A284413
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Exponent of 3 in 2^n + 1.
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1
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1, 0, 2, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 4, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 5, 0, 1, 0, 1, 0, 2
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OFFSET
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1,3
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COMMENTS
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Records: a(3^(n-1)) = n and a(k) < n for k < 3^(n-1).
Multiplicative because A051064 is. - Andrew Howroyd, Jul 28 2018
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Indranil Ghosh)
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FORMULA
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a(n) = A051064(n) if n is odd, 0 otherwise.
Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3/2. - Amiram Eldar, Sep 11 2020
From Amiram Eldar, Dec 27 2022: (Start)
Multiplicative with a(2^e) = 0, a(3^e) = e+1, and a(p^e) = 1 if p >= 5.
Dirichlet g.f.: zeta(s)*(1-1/2^s)/(1-1/3^s). (End)
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EXAMPLE
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a(27) = 4 because 2^27 + 1 = 134217729 = 3^4 * 19 * 87211.
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MATHEMATICA
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Table[If[OddQ[n], IntegerExponent[3n, 3], 0], {n, 100}] (* Indranil Ghosh, Mar 27 2017 *)
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PROG
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(Magma) [IsEven(n) select 0 else Factorization(3*n)[1][2]: n in [1..87]];
(PARI) a(n) = if(n%2, if(n<1, 0, 1 + valuation(n, 3)), 0); \\ Indranil Ghosh, Mar 27 2017
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CROSSREFS
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Cf. A051064, A168570 (exponent of 3 in 2^n - 1).
Sequence in context: A067432 A192174 A262202 * A323879 A129308 A159200
Adjacent sequences: A284410 A284411 A284412 * A284414 A284415 A284416
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KEYWORD
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nonn,mult,easy
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AUTHOR
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Jon E. Schoenfield, Mar 26 2017
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STATUS
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approved
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