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 A049226 #37 Mar 31 2025 13:32:15
%S A049226 119,527,1196,3591,5831,6887,12319,15407,18575,33271,47959,51119,
%T A049226 56853,63119,65151,116399,176911,328151,373319,437999,438311,520319,
%U A049226 568519,724687,734111,851927,957551,1059191,1140071,1437599,1760831,1813511,2320919,3354479,3383420
%N A049226 Composite numbers n such that the sum of divisors of n, sigma(n), divided by the number of divisors, d(n) and sigma(n) minus n are both rational squares.
%C A049226 The prime numbers with this property are primes of the form 2*k^2 - 1 (A066436). - _Amiram Eldar_, Aug 15 2019
%C A049226 The first terms for which the ratio sigma(n)/d(n) is not an integer are 267910912, 1398459816, and 1703794876. - _Giovanni Resta_, Aug 30 2019
%H A049226 Giovanni Resta, <a href="/A049226/b049226.txt">Table of n, a(n) for n = 1..1000</a> (first 300 terms from Amiram Eldar)
%e A049226 a(27) = 957551 is a term since the sum of its 16 divisors is sigma(957551) = 1166400 and both 1166400/16 = 72900 = 270^2 and 1166400 - 957551 = 208849 = 457^2 are perfect squares.
%t A049226 Select[Range[10^5], CompositeQ[#] && And @@ IntegerQ /@ Sqrt[{(s = DivisorSigma[1, #]) * DivisorSigma[0, #], s - #}] &] (* _Amiram Eldar_, Aug 15 2019 *)
%t A049226 cnQ[n_]:=With[{sg=DivisorSigma[1,n]},CompositeQ[n]&&AllTrue[{Sqrt[sg/DivisorSigma[0,n]],Sqrt[sg-n]},IntegerQ]]; Select[Range[ 339*10^4],cnQ] (* _Harvey P. Dale_, Mar 31 2025 *)
%o A049226 (PARI) is(n) = my(f = factor(n), s = sigma(f), nd = numdiv(f)); issquare(s/nd) && issquare(s - n) && !isprime(n) \\ _David A. Corneth_, Aug 15 2019
%o A049226 (Magma) [m:m in [1..3400000]|not IsPrime(m) and IsSquare(SumOfDivisors(m)/#Divisors(m)) and IsSquare(SumOfDivisors(m)-m)]; // _Marius A. Burtea_, Aug 15 2019
%Y A049226 Cf. A000005, A000203, A049207, A049227, A049228, A048699, A066436.
%K A049226 nonn
%O A049226 1,1
%A A049226 _Enoch Haga_
%E A049226 Name and offset corrected by _Amiram Eldar_, Aug 15 2019