OFFSET
1,2
COMMENTS
The Dirichlet convolution square of this sequence is A165825.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
FORMULA
MATHEMATICA
f[p_, e_] := Binomial[2*e, e]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Apr 30 2023 *)
PROG
(PARI) a(n)={my(v=factor(n)[, 2]); prod(i=1, #v, binomial(2*v[i], v[i]))}
(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<n, u[d]*u[n/d], 0)))/2); u}
DirSqrt(vector(80, n, 4^bigomega(n)))
(PARI) A317848(n) = factorback(apply(e -> binomial(e+e, e), factor(n)[, 2])); \\ Antti Karttunen, Sep 17 2018
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Andrew Howroyd, Aug 08 2018
STATUS
approved