login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A318449 Numerators of the sequence whose Dirichlet convolution with itself yields A001511, the 2-adic valuation of 2n. 3
1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 3, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 3, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 35, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A001511(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

MATHEMATICA

a1511[n_] := IntegerExponent[2n, 2];

f[1] = 1; f[n_] := f[n] = 1/2 (a1511[n] - Sum[f[d] f[n/d], {d, Divisors[ n][[2 ;; -2]]}]);

Table[f[n] // Numerator, {n, 1, 105}] (* Jean-François Alcover, Sep 13 2018 *)

PROG

(PARI)

up_to = 65537;

A001511(n) = 1+valuation(n, 2);

DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] - sumdiv(n, d, if(d>1&&d<n, u[d]*u[n/d], 0)))/2); u}; \\ From A317937.

v318449_51 = DirSqrt(vector(up_to, n, A001511(n)));

A318449(n) = numerator(v318449_51[n]);

CROSSREFS

Cf. A001511, A318450 (denominators).

Sequence in context: A031244 A030576 A101874 * A066715 A082457 A031178

Adjacent sequences:  A318446 A318447 A318448 * A318450 A318451 A318452

KEYWORD

nonn,frac

AUTHOR

Antti Karttunen and Andrew Howroyd, Aug 29 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 21 02:02 EDT 2019. Contains 325189 sequences. (Running on oeis4.)