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A135974
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a(n) = the smallest integer m > n such that d(m) > d(n), where d(n) = number of divisors of n.
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1
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2, 4, 4, 6, 6, 12, 8, 12, 10, 12, 12, 24, 14, 16, 16, 18, 18, 24, 20, 24, 24, 24, 24, 36, 26, 28, 28, 30, 30, 36, 32, 36, 36, 36, 36, 48, 38, 40, 40, 48, 42, 48, 44, 48, 48, 48, 48, 60, 50, 54, 52, 54, 54, 60, 56, 60, 60, 60, 60, 120, 62, 63, 64, 66, 66, 72, 68, 70, 70
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(6)=12 because 6 has 4 divisors and the smallest integer > 6 which has more than 4 divisors is 12.
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MAPLE
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with(numtheory): a:=proc (n) local m: for m from n+1 while tau(m) <= tau(n) do end do: m end proc: seq(a(n), n=1..60); # Emeric Deutsch, Mar 21 2008
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MATHEMATICA
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a = {}; For[n = 1, n < 70, n++, i = n + 1; While[ ! DivisorSigma[0, i] > DivisorSigma[0, n], i++ ]; AppendTo[a, i]]; a (* Stefan Steinerberger, Mar 16 2008 *)
simd[n_]:=Module[{m=n+1, d=DivisorSigma[0, n]}, While[DivisorSigma[0, m]<=d, m++]; m]; Array[simd, 70] (* Harvey P. Dale, Oct 03 2021 *)
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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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