OFFSET
1,2
COMMENTS
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..16384
FORMULA
a(n) = denominator of f(n), where f(1) = 1, f(n) = (1/2) * (A068068(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.
a(n) = 2^A318315(n).
From Antti Karttunen, Sep 03-07 2018: (Start, conjectured formulas)
a(n) = A006519(n) * A317934(n), thus multiplicative with a(2^e) = 2^A005187(e), a(p^e) = 2^A011371(e) for odd primes p.
(End)
MATHEMATICA
a35[n_] := (1 - (-1)^n)/2;
a120[n_] := DigitCount[n, 2, 1];
a[n_] := Product[{p, e} = pe; 2^(((2 - a35[p])*e) - a120[e]), {pe, FactorInteger[n]}];
a /@ Range[100] (* Jean-François Alcover, Sep 19 2019 *)
PROG
CROSSREFS
KEYWORD
nonn,frac,mult
AUTHOR
Antti Karttunen and Andrew Howroyd, Aug 29 2018
STATUS
approved