The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A299149 Numerators of the positive solution to n = Sum_{d|n} a(d) * a(n/d). 9
 1, 1, 3, 3, 5, 3, 7, 5, 27, 5, 11, 9, 13, 7, 15, 35, 17, 27, 19, 15, 21, 11, 23, 15, 75, 13, 135, 21, 29, 15, 31, 63, 33, 17, 35, 81, 37, 19, 39, 25, 41, 21, 43, 33, 135, 23, 47, 105, 147, 75, 51, 39, 53, 135, 55, 35, 57, 29, 59, 45, 61, 31, 189, 231, 65, 33 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Dirichlet convolution of a(n)/A046644(n) with itself yields A000265. - Antti Karttunen, Aug 30 2018 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 (first 1000 terms Andrew Howroyd) Wikipedia, Dirichlet convolution FORMULA a(n) = numerator(n*A317848(n)/A165825(n)) = A000265(n*A317848(n)). - Andrew Howroyd, Aug 09 2018 EXAMPLE Sequence begins: 1, 1, 3/2, 3/2, 5/2, 3/2, 7/2, 5/2, 27/8, 5/2, 11/2, 9/4, 13/2, 7/2. MATHEMATICA nn=50; sys=Table[n==Sum[a[d]*a[n/d], {d, Divisors[n]}], {n, nn}]; Numerator[Array[a, nn]/.Solve[sys, Array[a, nn]][[2]]] PROG (PARI) a(n)={my(v=factor(n)[, 2]); numerator(n*prod(i=1, #v, my(e=v[i]); binomial(2*e, e)/4^e))} \\ Andrew Howroyd, Aug 09 2018 (PARI) \\ DirSqrt(v) finds u such that v = v[1]*dirmul(u, u). 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

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.

Last modified June 13 00:57 EDT 2021. Contains 344980 sequences. (Running on oeis4.)