OFFSET
1,2
COMMENTS
a(n) = denominator of Sum_{d|n} 1/A000203(d).
Are there numbers n > 1 such that Sum_{d|n} 1/sigma(d) is an integer?
a(n) = 2 for n = 14, 244, 494, 45994. Are there any others? - Robert Israel, Apr 02 2017
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
EXAMPLE
For n = 6; divisors d of 6: {1, 2, 3, 6}; sigma(d): {1, 3, 4, 12}; Sum_{d|6} 1/sigma(d) = 1/1 + 1/3 + 1/4 + 1/12 = 20/12 = 5/3; a(n) = 3.
MAPLE
f:= n -> denom(add(1/numtheory:-sigma(d), d = numtheory:-divisors(n))):
map(f, [$1..200]); # Robert Israel, Apr 02 2017
MATHEMATICA
Table[Denominator[Plus@@(1/DivisorSigma[1, Divisors[n]])], {n, 70}] (* Alonso del Arte, Dec 24 2015 *)
PROG
(PARI) a(n) = denominator(sumdiv(n, d, 1/sigma(d))); \\ Michel Marcus, Feb 06 2024
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Dec 24 2015
STATUS
approved