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 A342104 #43 Dec 01 2024 03:41:11
%S A342104 2,12,18630,27000,443394,6242022,14412720,22315419,26744100,44630838,
%T A342104 50496960,106034880,128710944,148536990,162907584,212072880,218470770,
%U A342104 296259930,349444530,397253968,535267776,641250900,641418960,666274653,684165552,688208724,709639408
%N A342104 Balanced numbers (A020492) that are not arithmetic numbers (A003601).
%C A342104 Equivalently, numbers m such that phi(m) divides sigma(m) but tau(m) does not divide sigma(m), the corresponding quotients sigma(m)/phi(m) = A023897(m).
%C A342104 The only prime in the sequence is 2, because sigma(2)/phi(2) = 3 and sigma(2)/tau(2) = 3/2; then, if p odd prime, sigma(p)/phi(p) = (p+1)/(p-1) is an integer iff p = 3, but for p = 3, tau(3) divides sigma(3) with sigma(3)/tau(3) = 4/2 = 2.
%H A342104 Amiram Eldar, <a href="/A342104/b342104.txt">Table of n, a(n) for n = 1..5620</a>
%e A342104 Sigma(12) = 28, phi(12) = 4 and tau(12) = 6, hence phi(12) divides sigma(12), but tau(12) does not divide sigma(12), so 12 is a term.
%p A342104 with(numtheory): filter:= q -> (sigma(q) mod phi(q) = 0) and (sigma(q) mod tau(q) <> 0) : select(filter, [$1..500000]);
%t A342104 Select[Range[500000], Divisible[DivisorSigma[1, #], {DivisorSigma[0, #], EulerPhi[#]}] == {False, True} &] (* _Amiram Eldar_, Feb 28 2021 *)
%o A342104 (PARI) isok(m) = my(s=sigma(m)); !(s % eulerphi(m)) && (s % numdiv(m)); \\ _Michel Marcus_, Mar 01 2021
%Y A342104 Equals A020492 \ A003601.
%Y A342104 Cf. A000005 (tau), A000010 (phi), A000203 (sigma), A023897 (sigma/phi).
%Y A342104 Cf. A342103, A342105, A342106.
%K A342104 nonn
%O A342104 1,1
%A A342104 _Bernard Schott_, Feb 28 2021
%E A342104 a(5)-a(27) from _Amiram Eldar_, Feb 28 2021