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%I #11 Sep 08 2022 08:46:09
%S 1,672,4680,30240,23569920,45532800,275890944,14182439040,
%T 153003540480,403031236608,518666803200
%N Numbers n such that k(n) = (n/tau(n) + sigma(n)/n) is an integer.
%C Numbers n such that A245784(n) / A245785(n) = (n / A000005(n) + A000203(n) / n) is an integer.
%C Sequence of numbers k(n): 2, 31, 101, 319, 73660, 118579, …
%C Conjecture: Subsequence of A216793.
%C Refactorable multiply-perfect numbers (A245782) are members of this sequence.
%C a(12) > 10^13. - _Giovanni Resta_, Jul 13 2015
%F A245785(a(n)) = 1.
%e 672 is in sequence because 672/tau(672) + sigma(672)/672 = 672/24 + 2016/672 = 31 (integer).
%o (Magma) [n: n in [1..100000] | (Denominator((n/(#[d: d in Divisors(n)])) + (SumOfDivisors(n)/n)) eq 1)]
%o (PARI) for(n=1, 10^8, s=n/numdiv(n); t=sigma(n)/n; if(floor(s+t)==s+t, print1(n, ", "))) \\ _Derek Orr_, Aug 15 2014
%Y Cf. A000005, A000203, A245784, A245785, A245782.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Aug 15 2014
%E a(7)-a(11) from _Giovanni Resta_, Jul 13 2015