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.
n=7: p(7) = 17. a(7) = 416640 = 2^7*3*5*7*31. sigma(416640) = 1566720 = 17*phi(a(7)). phi(416640) = 92160.
a(29)=5284804 because sigma(5284804)=29*pi(5284804) and 5284804 is the smallest such number.
For n = 4; a(4) = 6 because 6 is the smallest number with sigma(6) / phi(6) = 12 / 2 = 6 >= 2.
a:=1; S:=[a]; for n in [2..24] do k:=0; flag:= true; while flag do k+:=1; if &+[d: d in Divisors(k)] / EulerPhi(k) ge n then Append(~S, k); a:=k; flag:=false; end if; end while; end for; S;
b:= 0:
for n from 1 to 3*10^6 do
r:= floor(numtheory:-sigma(n)/numtheory:-phi(n));
if r > b then
for i from b+1 to r do A[i]:= n od:
b:= r;
fi
od:
seq(A[i],i=1..b); # Robert Israel, Aug 21 2017
With[{s = KeySort@ PositionIndex@ Array[Floor[DivisorSigma[1, #]/EulerPhi@ #] &, 10^6]}, Function[t, Reverse@ FoldList[Min, #] &@ Reverse@ TakeWhile[#, # > 0 &] &@ ReplacePart[t, Map[# -> Lookup[s, #][[1]] &, Keys@ s]]]@ ConstantArray[0, Max@ Keys@ s]] (* Michael De Vlieger, Aug 19 2017 *) (* or *)
r = 1; Reap[ Do[z = DivisorSigma[1, n]/EulerPhi@ n; While[z >= r, r++; Sow@ n], {n, 10^6}]][[2, 1]] (* Giovanni Resta, Aug 21 2017 *)
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