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.
180 is a term since sigma(180) - 3*180 = 6 > 0 and 180 is divisible by 6.
Select[Range[27000], (d = DivisorSigma[1, #] - 3*#) > 0 && Divisible[#, d] &]
is(n) = {my(d = sigma(n) - 3*n); d > 0 && n%d == 0;}
6 is a term because sigma(6)/6 - 1 = 2 - 1 = 1, a square; like for all perfect numbers. 9 is a term because sigma(9)/9 - 1 = 13/9 - 1 = 4/9, a square.
q[k_] := And @@ IntegerQ /@ Sqrt[NumeratorDenominator[DivisorSigma[-1, k] - 1]]; Select[Range[2*10^6], q] (* Amiram Eldar, Apr 28 2025 *)
isok(k) = issquare(sigma(k)/k - 1);
216 is a term since sigma(216)/216 - 1 = (4/3)^2 and sigma(12)/12 - 1 = 4/3.
isok(k)=my(t=(sigma(k)-k)*k); if(issquare(t), my(r=sqrtint(t)/k+1, s=denominator(r)); forstep(m=s, k, s, if(sigma(m)/m==r, return(1)) )); 0 \\ Andrew Howroyd, Mar 03 2025
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