cp's OEIS Frontend

A306639 Numbers m such that Sum_{d|m} (sigma(d)/tau(d)) is an integer h where sigma(k) = the sum of the divisors of k (A000203) and tau(k) = the number of divisors of k (A000005).

%I A306639 #17 Sep 08 2022 08:46:21
%S A306639 1,3,5,7,10,11,13,15,17,19,21,23,26,29,30,31,33,34,35,37,39,41,43,47,
%T A306639 49,51,53,55,57,58,59,60,61,65,67,69,70,71,73,74,75,77,78,79,82,83,85,
%U A306639 87,89,91,93,95,97,98,101,102,103,105,106,107,109,110,111,113
%N A306639 Numbers m such that Sum_{d|m} (sigma(d)/tau(d)) is an integer h where sigma(k) = the sum of the divisors of k (A000203) and tau(k) = the number of divisors of k (A000005).
%C A306639 Sum_{d|n} sigma(d)/tau(d) > 1 for all n > 1.
%C A306639 Sum_{d|n} sigma(d)/tau(d) = n only for numbers 1, 3, 10 and 30.
%C A306639 Odd primes are terms.
%C A306639 Corresponding values of integers h: 1, 3, 4, 5, 10, 7, 8, 12, 10, 11, 15, 13, 20, 16, 30, 17, 21, 25, 20, 20, 24, ...
%F A306639 A324500(a(n)) = 1.
%e A306639 Sum_{d|n} sigma(d)/tau(d) for n >= 1: 1, 5/2, 3, 29/6, 4, 15/2, 5, 103/12, 22/3, 10, 7, 29/2, 8, 25/2, 12, 887/60, ...
%e A306639 10 is a term because Sum_{d|10} (sigma(d)/tau(d)) = sigma(1)/tau(1) + sigma(2)/tau(2) + sigma(5)/tau(5) + sigma(10)/tau(10) = 1/1 + 3/2 + 6/2 + 18/4 = 10 (integer).
%o A306639 (Magma) [n: n in [1..1000] | Denominator(&+[SumOfDivisors(d) / NumberOfDivisors(d): d in Divisors(n)]) eq 1]
%o A306639 (PARI) isok(n) = frac(sumdiv(n, d, sigma(d)/numdiv(d))) == 0; \\ _Michel Marcus_, Mar 03 2019
%Y A306639 Cf. A000005, A000203, A324499, A324500.
%K A306639 nonn
%O A306639 1,2
%A A306639 _Jaroslav Krizek_, Mar 02 2019