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.
\\ See A134382.
For n=20, sigma(20)/(d(20)*sopf(20)) = 42/(6*7) = 1, an integer, so 20 is a term.
[k: k in [2..2100]|IsIntegral(DivisorSigma(1,k)/(#Divisors(k)*(&+PrimeDivisors(k))))]; // Marius A. Burtea, Oct 03 2019
f[p_, e_] := (p^(e + 1) - 1)/((e + 1)*(p - 1)); Select[Range[2, 2100], IntegerQ[ Times @@ (f @@@ (fct = FactorInteger[#])) / Plus @@ (fct[[;; , 1]])] &] (* Amiram Eldar, Oct 03 2019 *)
sopf(f) = sum(j=1, #f~, f[j, 1]); \\ A008472 isok(m) = if (m>1, my(f=factor(m)); (sigma(f) % (numdiv(f)*sopf(f))) == 0);
For A328052(1)=20, sigma(20)/(d(20)*sopf(20)) = 42/(6*7) = 1, so a(1) = 1.
[a: k in [2..5000]|IsIntegral(a) where a is DivisorSigma(1,k)/(#Divisors(k)*(&+PrimeDivisors(k)))]; // Marius A. Burtea, Oct 03 2019
f[p_, e_] := (p^(e + 1) - 1)/((e + 1)*(p - 1)); r[n_] := Times @@ (f @@@ (fct = FactorInteger[n])) / Plus @@ (fct[[;; , 1]]); Select[r /@ Range[2, 4500], IntegerQ] (* Amiram Eldar, Oct 03 2019 *)
lista(nn) = {for (n=2, nn, my(f=factor(n)); if (denominator(q = sigma(f)/(numdiv(f)*sopf(f))) == 1, print1(q, ", ")););}
sopf(f) = sum(j=1, #f~, f[j, 1]); \\ A008472 isok(k, n) = my(fk=factor(k)); n*numdiv(fk)*sopf(fk) == sigma(fk); a(n) = {my(k=1); while (!isok(k, n), k++); k;}
sopf(f) = sum(j=1, #f~, f[j, 1]); \\ A008472 lista(nn) = {/* nn should be > 10^7 */ my(nmax = 43, v = vector(nmax, k, List())); for (n=2, nn, my(f=factor(n), q); if (denominator(q=sigma(f)/(numdiv(f)*sopf(f))) == 1, if (q <= nmax, listput(v[q], n)););); for (i=1, nmax, if (#v[i] == 0, break); print1(vecmax(Vec(v[i])), ", "););}
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