login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A265710
a(n) = denominator of Sum_{d|n} 1/sigma(d).
10
1, 3, 4, 21, 6, 3, 8, 35, 52, 9, 12, 84, 14, 2, 24, 1085, 18, 13, 20, 18, 32, 9, 24, 14, 186, 7, 520, 56, 30, 18, 32, 9765, 48, 27, 16, 364, 38, 5, 56, 5, 42, 8, 44, 252, 104, 18, 48, 868, 456, 279, 72, 98, 54, 390, 72, 140, 16, 45, 60, 72, 62, 8, 416, 1240155
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
FORMULA
a(1) = 1; a(p) = p + 1 for p = prime.
a(n) = A265709(n) / (Sum_{d|n} 1/sigma(d)) = A265709(n) * A069934(n) / A265708(n).
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
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Dec 24 2015
STATUS
approved