OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
For n = 4, 4 has 2 unitary divisors, 1 and 4. Their unitary abundancy indices are usigma(1)/1 = 1 and usigma(4)/4 = 5/4, and their mean unitary abundancy index is (1 + 5/4)/2 = 9/8. Therefore a(4) = denominator(9/8) = 8.
MATHEMATICA
f[p_, e_] := 1 + 1/(2*p^e); a[1] = 1; a[n_] := Denominator[Times @@ f @@@ FactorInteger[n]]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n)); denominator(prod(i = 1, #f~, 1 + 1/(2*f[i, 1]^f[i, 2]))); }
CROSSREFS
KEYWORD
nonn,easy,frac
AUTHOR
Amiram Eldar, Jul 20 2024
STATUS
approved