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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