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A291185
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a(n) = the smallest number k such that sigma(k) / phi(k) >= n.
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0
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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
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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For n = 4; a(4) = 6 because 6 is the smallest number with sigma(6) / phi(6) = 12 / 2 = 6 >= 2.
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MAPLE
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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:
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MATHEMATICA
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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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PROG
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(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;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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