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 A068991 #35 Sep 08 2022 08:45:05
%S A068991 1,2,3,6,10,21,30,42,78,110,210,330,390,930,1218,1830,2025,2310,2530,
%T A068991 4050,4134,4290,6090,7590,14175,14910,22110,28350,51090,52650,53130,
%U A068991 66990,71862,98670,118910,159975,214650,319950,356730,359310,442338,635850,684450
%N A068991 Numbers k such that Sum_{d divides k} sigma(d)/phi(d) is an integer.
%C A068991 Conjecture: if k is in the sequence and k is squarefree then the denominator of the 2k-th Bernoulli's number contains k. E.g., 2310 is squarefree, is in the sequence and A002445(2310)=744535159372016163713900138929458330 is divisible by 2310.
%C A068991 For the first 74 terms, the largest k < n such that a(k) | a(n) is close to n. Is it sufficient to assume a(k) * m = a(n) to find the next terms merely recursively? If so, how large do we choose m? - _David A. Corneth_, Oct 11 2019
%C A068991 Six other terms are 240998502150, 275082346350, 1660078844550, 2170540451310, 13878528210690, 722754507947850. - _David A. Corneth_, Oct 21 2019
%H A068991 Amiram Eldar, <a href="/A068991/b068991.txt">Table of n, a(n) for n = 1..74</a>
%t A068991 aQ[n_] := IntegerQ @ DivisorSum[n, DivisorSigma[1, #]/EulerPhi[#] &]; Select[
%t A068991 Range[10000], aQ] (* _Amiram Eldar_, Oct 05 2019 *)
%o A068991 (PARI) isok(n) = denominator(sumdiv(n, d, sigma(d)/eulerphi(d))) == 1; \\ _Michel Marcus_, Dec 07 2013
%o A068991 (Magma) [k:k in [1..600000]| IsIntegral(&+[ DivisorSigma(1,d)/EulerPhi(d):d in Divisors(k)])]; // _Marius A. Burtea_, Oct 10 2019
%K A068991 nonn
%O A068991 1,2
%A A068991 _Benoit Cloitre_, Apr 06 2002
%E A068991 More terms from _Michel Marcus_, Dec 07 2013