cp's OEIS Frontend

A276736 a(n) = numerator of Sum_{d|n} tau(d)/d.

%I A276736 #21 Sep 08 2022 08:46:17
%S A276736 1,2,5,11,7,10,9,13,2,14,13,55,15,18,7,57,19,4,21,77,15,26,25,65,38,
%T A276736 30,58,99,31,14,33,15,65,38,9,11,39,42,25,91,43,30,45,13,14,50,49,95,
%U A276736 66,76,95,165,55,116,91,117,35,62,61,77,63,66,18,247,21,130
%N A276736 a(n) = numerator of Sum_{d|n} tau(d)/d.
%C A276736 Also numerators of (Sum_{d|n} sigma(d)) / n.
%H A276736 Jaroslav Krizek, <a href="/A276736/b276736.txt">Table of n, a(n) for n = 1..1000</a>
%F A276736 For all n we have: n = (Sum_{d|n} sigma(d)) / (Sum_{d|n} tau(d)/d) = (Sum_{d|n} d*tau(n/d)) / (Sum_{d|n} tau(d)/d) = A007429(n) * A276737(n) / a(n).
%e A276736 For n=6; {d_6} = {1, 2, 3, 6}; {tau(d)_6} = {1, 2, 2, 4};  Sum_{d|6} tau(d)/d = 1/1 + 2/2 + 2/3 + 4/6 = 20/6 = 10/3; a(6) = 10.
%e A276736 For n=6; {d_6} = {1, 2, 3, 6}; {sigma(d)_6} = {1, 3, 4, 12};  (Sum_{d|6} sigma(d))/6 = (1+3+4+12)/6 = 10/3; a(6) = 10.
%t A276736 Table[Numerator@ Total[DivisorSigma[0, #]/#] &@ Divisors@ n, {n, 66}] (* _Michael De Vlieger_, Sep 16 2016 *)
%o A276736 (Magma) [Numerator(&+[NumberOfDivisors(d)/d: d in Divisors(n)]): n in [1..100]]
%o A276736 (PARI) a(n) = numerator(sumdiv(n, d, numdiv(d)/d)); \\ _Michel Marcus_, Sep 16 2016
%Y A276736 Cf. A000005, A007429, A276737 (denominators).
%K A276736 nonn,frac
%O A276736 1,2
%A A276736 _Jaroslav Krizek_, Sep 16 2016