OFFSET
1,4
COMMENTS
Multiplicative because A064989 is.
No negative terms among the first 2^20 terms.
LINKS
FORMULA
a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A064989(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
PROG
(PARI)
up_to = 16384;
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); 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.
v318319aux = DirSqrt(vector(up_to, n, A064989(n)));
A318319(n) = numerator(v318319aux[n]);
CROSSREFS
KEYWORD
nonn,frac,mult
AUTHOR
Antti Karttunen, Aug 24 2018
STATUS
approved