A291185 a(n) = the smallest number k such that sigma(k) / phi(k) >= n.

1, 2, 2, 6, 6, 6, 12, 30, 30, 60, 120, 210, 420, 420, 840, 2520, 9240, 9240, 27720, 55440, 120120, 360360, 720720, 2162160, 6126120, 12252240, 36756720, 116396280, 232792560, 698377680, 2677114440, 5354228880, 26771144400, 155272637520, 465817912560

Offset: 1

Author

Jaroslav Krizek, Aug 19 2017

Keywords

• nonn

Comments

a(n) = the smallest number k such that A000203(k) / A000010(k) = A289336(k) / A289412(k) >= n.

Examples

			For n = 4; a(4) = 6 because 6 is the smallest number with sigma(6) / phi(6) = 12 / 2 = 6 >= 2.
		

Crossrefs

Cf. A000010, A000203, A055234, A289336, A289412.

Programs

Magma

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;

Maple

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

Mathematica

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 *)

Extensions

a(25)-a(35) from Giovanni Resta, Aug 21 2017