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

%S 1,3,3,11,3,9,3,25,11,9,3,11,3,9,9,137,3,11,3,11,9,9,3,25,11,9,25,11,

%T 3,27,3,49,9,9,9,121,3,9,9,25,3,27,3,11,11,9,3,137,11,11,9,11,3,25,9,

%U 25,9,9,3,33,3,9,11,363,9,27,3,11,9,27,3,275,3,9,11

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

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

%H G. C. Greubel, <a href="/A265391/b265391.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n) = [Sum_{d|n} 1 / tau(d)] * A265392(n) = A265390(n) * A265392(n) / A253139(n).

%F a(1) = 1; a(p) = 3 for p = prime.

%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) = 9 (numerator).

%t Table[Numerator[Sum[1/DivisorSigma[0, d], {d, Divisors@ n}]], {n, 75}] (* _Michael De Vlieger_, Dec 09 2015 *)

%o (Magma) [Numerator(&+[1/NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]]

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

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

%K nonn,frac

%O 1,2

%A _Jaroslav Krizek_, Dec 08 2015