%I #16 Sep 08 2022 08:46:14

%S 1,2,2,6,2,4,2,12,6,4,2,4,2,4,4,60,2,4,2,4,4,4,2,8,6,4,12,4,2,8,2,20,

%T 4,4,4,36,2,4,4,8,2,8,2,4,4,4,2,40,6,4,4,4,2,8,4,8,4,4,2,8,2,4,4,140,

%U 4,8,2,4,4,8,2,72,2,4,4,4,4,8,2,40,60,4,2

%N a(n) = denominator of Sum_{d|n} 1 / tau(d).

%C a(n) = denominator of Sum_{d|n} 1 / A000005(d).

%H G. C. Greubel, <a href="/A265392/b265392.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n) = A265391(n) / [Sum_{d|n} 1 / tau(d)] = A265391(n) * A253139(n) / A265390(n).

%F a(1) = 1; a(p) = 2 for p = prime; a(n) = n for numbers 1, 2, 36, 72, ...

%e For n = 6; divisors d of 6: {1, 2, 3, 6}; tau(d): {1, 2, 2, 4}; Sum_{d|6} 1 / tau(d) = 1/1 + 1/2 + 1/2 + 1/4 = 9 / 4; a(n) = 4 (denominator).

%t Table[Denominator[Sum[1/DivisorSigma[0, d], {d, Divisors@ n}]], {n, 83}] (* _Michael De Vlieger_, Dec 09 2015 *)

%o (Magma) [Denominator(&+[1/NumberOfDivisors(d): d in Divisors(n)]): n in [1..1000]]

%o (PARI) a(n) = denominator(sumdiv(n, d, 1/numdiv(d))); \\ _Michel Marcus_, Dec 09 2015

%Y Cf. A000005, A253139, A265390, A265391 (numerator), A265392, A265393.

%K nonn,frac

%O 1,2

%A _Jaroslav Krizek_, Dec 08 2015