A183039 a(n) = A051064(n)*3^A051064(n) where A051064(n) equals the 3-adic valuation of 3n.

3, 3, 18, 3, 3, 18, 3, 3, 81, 3, 3, 18, 3, 3, 18, 3, 3, 81, 3, 3, 18, 3, 3, 18, 3, 3, 324, 3, 3, 18, 3, 3, 18, 3, 3, 81, 3, 3, 18, 3, 3, 18, 3, 3, 81, 3, 3, 18, 3, 3, 18, 3, 3, 324, 3, 3, 18, 3, 3, 18, 3, 3, 81, 3, 3, 18, 3, 3, 18, 3, 3, 81, 3, 3, 18, 3, 3, 18, 3, 3, 1215, 3, 3, 18, 3, 3, 18, 3, 3, 81

Offset

1,1

Comments

3^A051064(n) exactly divides 3n.

Links

Table of n, a(n) for n=1..90.

Formula

Logarithmic derivative of A183038.

Example

L.g.f.: A(x) = 3*x + 3*x^2/2 + 18*x^3/3 + 3*x^4/4 + 3*x^5/5 + 18*x^6/6 + 3*x^7/7 + 3*x^8/8 + 81*x^9/9 + 3*x^10/10 + 3*x^11/11 + 18*x^12/12 +...
The g.f. of A183038 begins:
exp(A(x)) = 1 + 3*x + 6*x^2 + 15*x^3 + 30*x^4 + 51*x^5 + 93*x^6 +...

Prog

(PARI) {a(n)=valuation(3*n, 3)*3^valuation(3*n, 3)}

Crossrefs

Cf. A183038, A183037.

Sequence in context: A215076 A095106 A130184 * A192527 A227773 A346380

Adjacent sequences: A183036 A183037 A183038 * A183040 A183041 A183042

Keyword

nonn

Author

Paul D. Hanna, Dec 19 2010

Status

approved