OFFSET
1,3
COMMENTS
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..16384
FORMULA
a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A235199(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
PROG
(PARI)
up_to = 16384;
A235199(n) = if(n<=4, n, my(f = factor(n)); for(i=1, #f~, if(5==f[i, 1], f[i, 1] += 2, if(7==f[i, 1], f[i, 1] -= 2, my(k=primepi(f[i, 1])); if(k>4, f[i, 1] = prime(A235199(k)))))); factorback(f));
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.
v317929aux = DirSqrt(vector(up_to, n, A235199(n)));
A317929(n) = numerator(v317929aux[n]);
CROSSREFS
KEYWORD
nonn,frac,mult
AUTHOR
Antti Karttunen, Aug 23 2018
STATUS
approved