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