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A284413 Exponent of 3 in 2^n + 1. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Records: a(3^(n-1)) = n and a(k) < n for k < 3^(n-1).

Multiplicative because A051064 is. - Andrew Howroyd, Jul 28 2018

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Indranil Ghosh)

FORMULA

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)

EXAMPLE

a(27) = 4 because 2^27 + 1 = 134217729 = 3^4 * 19 * 87211.

MATHEMATICA

Table[If[OddQ[n], IntegerExponent[3n, 3], 0], {n, 100}] (* Indranil Ghosh, Mar 27 2017 *)

PROG

(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

CROSSREFS

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

KEYWORD

nonn,mult,easy

AUTHOR

Jon E. Schoenfield, Mar 26 2017

STATUS

approved

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Last modified February 1 06:22 EST 2023. Contains 359981 sequences. (Running on oeis4.)