OFFSET
1,256
COMMENTS
First term greater than 1 in absolute value is a(256) = 2.
LINKS
FORMULA
Dirichlet g.f.: Product_{n > 1} 1/(1 + 1/n^s).
EXAMPLE
The factorizations of 24 are (2*2*2*3), (2*2*6), (2*3*4), (2*12), (3*8), (4*6), (24); so a(24) = 1 - 2 + 3 - 1 = 1.
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Table[Sum[(-1)^Length[f], {f, facs[n]}], {n, 200}]
PROG
(PARI) A316441(n, m=n, k=0) = if(1==n, (-1)^k, my(s=0); fordiv(n, d, if((d>1)&&(d<=m), s += A316441(n/d, d, k+1))); (s)); \\ Antti Karttunen, Sep 08 2018, after Michael B. Porter's code for A001055
CROSSREFS
KEYWORD
sign
AUTHOR
Gus Wiseman, Jul 03 2018
EXTENSIONS
Secondary offset added by Antti Karttunen, Sep 08 2018
STATUS
approved