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 A341781 #15 Feb 21 2021 02:27:47 %S A341781 8,12,36,72,80,96,128,180,240,252,288,384,396,448,468,480,560,612,640, %T A341781 672,684,720,828,864,880,896,972,1040,1044,1056,1116,1152,1200,1248, %U A341781 1332,1344,1360,1408,1440,1476,1520,1548,1620,1632,1664,1680,1692,1800,1824 %N A341781 Refactorable numbers (or tau numbers, A033950) k such that k/tau(k) is even, where tau(k) = A000005(k). %C A341781 Zelinsky (2002) called these numbers p-generators. He proved that these are the tau numbers k such that for any prime p, if p does not divide k then p*k is also a tau number. He used these numbers to prove that the number of tau numbers not exceeding m is > pi(m)/2 for all m > 7.42*10^13, where pi(m) = A000720(m). %H A341781 Amiram Eldar, <a href="/A341781/b341781.txt">Table of n, a(n) for n = 1..10000</a> %H A341781 Joshua Zelinsky, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL5/Zelinsky/zelinsky9.html">Tau Numbers: A Partial Proof of a Conjecture and Other Results</a>, Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.8. %e A341781 8 is a term since 8/tau(8) = 8/4 = 2 is even. %t A341781 q[n_] := Divisible[n, (d = DivisorSigma[0, n])] && EvenQ[n/d]; Select[Range[2000], q] %o A341781 (PARI) isok(k) = my(q=k/numdiv(k)); (denominator(q)==1) && ((q%2) == 0); \\ _Michel Marcus_, Feb 20 2021 %Y A341781 Cf. A000005, A000720, A033950, A036762, A039819, A281188. %K A341781 nonn %O A341781 1,1 %A A341781 _Amiram Eldar_, Feb 19 2021