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%I #13 Dec 15 2021 09:21:17
%S 2,3,4,6,6,8,8,10,10,12,12,18,14,15,16,18,18,20,20,24,22,24,24,30,26,
%T 27,28,30,30,36,32,36,34,35,36,48,38,39,40,42,42,48,44,45,48,48,48,60,
%U 50,52,52,54,54,56,56,60,58,60,60,72,62,63,64,66,66,70,68,70,70,72,72,84
%N Smallest number greater than n having at least as many divisors as n.
%C A000005(n) <= A000005(a(n)) and A000005(k) < A000005(n) for n<k<a(n);
%C A000005(2*k-1) <= A000005(2*k) for 1<=k<=22. - Corrected by _Robert Israel_, Jul 23 2019
%H Robert Israel, <a href="/A112275/b112275.txt">Table of n, a(n) for n = 1..10000</a>
%p N:= 1000: # for all terms before the first term > N
%p taus:= map(numtheory:-tau,[$1..N]):
%p for n from 1 to N do
%p found:= false:
%p for k from n+1 to N while not found do
%p if taus[k]>=taus[n] then found:= true; A[n]:= k fi
%p od;
%p if not found then break fi
%p od:
%p seq(A[i],i=1..n-1); # _Robert Israel_, Jul 23 2019
%t kmax[n_] := 2 n;
%t a[n_] := Module[{tau = DivisorSigma[0, n], k},
%t For[k = n + 1, k <= kmax[n], k++,
%t If[DivisorSigma[0, k] >= tau, Return[k]]];
%t Print["a(n) = k not found for n = ", n]];
%t Array[a, 100] (* _Jean-François Alcover_, Dec 15 2021 *)
%Y Cf. A079427, A112276.
%Y Cf. A138171 (odd n for which a(n) > n+1).
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Sep 01 2005
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