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%I #13 Oct 03 2021 12:18:09
%S 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,
%T 28,28,30,30,36,32,36,36,36,36,48,38,40,40,48,42,48,44,48,48,48,48,60,
%U 50,54,52,54,54,60,56,60,60,60,60,120,62,63,64,66,66,72,68,70,70
%N a(n) = the smallest integer m > n such that d(m) > d(n), where d(n) = number of divisors of n.
%H Harvey P. Dale, <a href="/A135974/b135974.txt">Table of n, a(n) for n = 1..1000</a>
%e a(6)=12 because 6 has 4 divisors and the smallest integer > 6 which has more than 4 divisors is 12.
%p 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
%t 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 *)
%t 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 *)
%Y Cf. A000005, A112275.
%K nonn
%O 1,1
%A _Leroy Quet_, Mar 02 2008
%E More terms from _Stefan Steinerberger_, Mar 16 2008
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