OFFSET
1,16
COMMENTS
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) * (A034444(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
PROG
(PARI)
A034444(n) = (2^omega(n));
A317933perA317934(n) = if(1==n, n, (A034444(n)-sumdiv(n, d, if((d>1)&&(d<n), A317933perA317934(d)*A317933perA317934(n/d), 0)))/2);
A317933(n) = numerator(A317933perA317934(n));
(PARI)
up_to = 65537;
\\ Faster:
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.
v317933aux = DirSqrt(vector(up_to, n, A034444(n)));
A317933(n) = numerator(v317933aux[n]);
CROSSREFS
KEYWORD
nonn,frac,mult
AUTHOR
Antti Karttunen, Aug 12 2018
STATUS
approved