This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A245778 #19 Sep 08 2022 08:46:09 %S A245778 1,672,4680,30240,435708,23569920,45532800,4138364160,14182439040, %T A245778 53798734080,153003540480,403031236608,518666803200 %N A245778 Numbers n such that k(n) = n/tau(n) - sigma(n)/n is an integer. %C A245778 Numbers n such that A245776(n) / A245777(n) = (n / A000005(n) - A000203(n) / n) is an integer. %C A245778 Sequence of integers k(n): 0, 25, 94, 311, 4031, 73652, 118571, … %C A245778 Conjecture: subsequence of A216793. %C A245778 Refactorable multiply-perfect numbers (A245782) are members of this sequence. %C A245778 a(14) > 10^13. - _Giovanni Resta_, Jul 13 2015 %C A245778 The numbers 13661860101120 and 740344994887680 are also terms. - _Giovanni Resta_, Nov 14 2019 %F A245778 A245777(a(n)) = 1. %e A245778 672 is in sequence because 672 / tau(672) - sigma(672) / 672 = 672 / 24 - 2016 / 672 = 25 (integer). %p A245778 select(n -> type(n/numtheory:-tau(n) - numtheory:-sigma(n)/n,integer), [$1..10^8]); # _Robert Israel_, Aug 03 2014 %o A245778 (Magma) [n: n in [1..100000] | (Denominator((n/(#[d: d in Divisors(n)])) - (SumOfDivisors(n)/n)) eq 1)] %o A245778 (PARI) %o A245778 for(n=1,10^8,s=n/numdiv(n);t=sigma(n)/n;if(floor(s-t)==s-t,print1(n,", "))) \\ _Derek Orr_, Aug 01 2014 %Y A245778 Cf. A000005, A000203, A216793, A245776, A245777, A245779, A245782. %K A245778 nonn,more %O A245778 1,2 %A A245778 _Jaroslav Krizek_, Aug 01 2014 %E A245778 a(8)-a(13) from _Giovanni Resta_, Jul 13 2015