cp's OEIS Frontend

A323781 Numbers m such that Sum_{d|m} (tau(d)/sigma(d)) is an integer h where tau(k) = the number of the divisors of k (A000005) and sigma(k) = the sum of the divisors of k (A000203).

%I A323781 #15 Sep 08 2022 08:46:23
%S A323781 1,15,429,609,6003,9156,20943,75579,90252,93849,115773,331359,631764,
%T A323781 744993,817191,837655,925083,1130766,1141191,2349087,2491740,2512965,
%U A323781 3040728,3266253,3796143,4314891,4365231,5025930,5294340,6135624,6629271,7210671,10906175
%N A323781 Numbers m such that Sum_{d|m} (tau(d)/sigma(d)) is an integer h where tau(k) = the number of the divisors of k (A000005) and sigma(k) = the sum of the divisors of k (A000203).
%C A323781 Sum_{d|n} (tau(d)/sigma(d)) > 1 for all n > 2.
%C A323781 Corresponding values of integers h: 1, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 5, 2, 2, 2, 2, 4, 2, 2, 5, 3, 4, 2, 2, 2, 2, 5, 5, 5, 2, 2, 2, ...
%C A323781 The smallest number m such that Sum_{d|m} (tau(d)/sigma(d)) is an integer h for h >= 1:  1, 15, 2512965, 9156, 631764, ...
%F A323781 A323780(a(n)) = 1.
%e A323781 15 is a term because Sum_{d|15} (tau(d)/sigma(d)) = tau(1)/sigma(1) + tau(3)/sigma(3) + tau(5)/sigma(5) + tau(15)/sigma(15) = 1/1 + 2/4 + 2/6 + 4/24 = 2 (integer).
%t A323781 Select[Range[10^5], IntegerQ@ DivisorSum[#, Divide @@ DivisorSigma[{0, 1}, #] &] &] (* _Michael De Vlieger_, Feb 17 2019 *)
%o A323781 (Magma) [n: n in [1..1000000] | Denominator(&+[NumberOfDivisors(d) / SumOfDivisors(d): d in Divisors(n)]) eq 1]
%o A323781 (PARI) isok(n) = !frac(sumdiv(n, d, numdiv(d)/sigma(d))); \\ _Michel Marcus_, Feb 16 2019
%Y A323781 Cf. A000005, A000203, A323779, A323780.
%K A323781 nonn
%O A323781 1,2
%A A323781 _Jaroslav Krizek_, Feb 16 2019