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%I #19 Feb 06 2024 09:38:50
%S 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,
%T 7,520,56,30,18,32,9765,48,27,16,364,38,5,56,5,42,8,44,252,104,18,48,
%U 868,456,279,72,98,54,390,72,140,16,45,60,72,62,8,416,1240155
%N a(n) = denominator of Sum_{d|n} 1/sigma(d).
%C a(n) = denominator of Sum_{d|n} 1/A000203(d).
%C Are there numbers n > 1 such that Sum_{d|n} 1/sigma(d) is an integer?
%C a(n) = 2 for n = 14, 244, 494, 45994. Are there any others? - _Robert Israel_, Apr 02 2017
%H Robert Israel, <a href="/A265710/b265710.txt">Table of n, a(n) for n = 1..10000</a>
%F a(1) = 1; a(p) = p + 1 for p = prime.
%F a(n) = A265709(n) / (Sum_{d|n} 1/sigma(d)) = A265709(n) * A069934(n) / A265708(n).
%e 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.
%p f:= n -> denom(add(1/numtheory:-sigma(d), d = numtheory:-divisors(n))):
%p map(f, [$1..200]); # _Robert Israel_, Apr 02 2017
%t Table[Denominator[Plus@@(1/DivisorSigma[1, Divisors[n]])], {n, 70}] (* _Alonso del Arte_, Dec 24 2015 *)
%o (PARI) a(n) = denominator(sumdiv(n, d, 1/sigma(d))); \\ _Michel Marcus_, Feb 06 2024
%Y Cf. A069934, A000203, A265708, A265709, A265711, A265712, A265713, A265714, A266227, A266228.
%K nonn,frac
%O 1,2
%A _Jaroslav Krizek_, Dec 24 2015
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