%I #4 Mar 30 2018 03:05:35
%S 6,14,10,14,16,20,21,33,24,28,20,30,33,30,34,30,54,40,24,42,44,42,66,
%T 30,48,42,60,57,68,44,54,40,60,66,54,52,63,85,102,74,66,104,88,66,80,
%U 60,84,99,93,96,86,114,76,132,105,102,60,88,111,90,138,105,114,102,105,138,96
%N Smallest positive integer k with the same sum of divisors as the n-th integer for which such a k exists.
%H Robert Israel, <a href="/A131902/b131902.txt">Table of n, a(n) for n = 1..10000</a>
%F Let S={n>0 : there exists a k>0 and k<n with sigma(k)=sigma(n)}. Then a(n):=min(k>0: sigma(k)=sigma(n-th element of S)
%e a(3)=10 because 17 is the third integer for which a smaller integer with same sum of divisors exists and sigma(17)=1+17=18 and sigma(10)=1+2+5+10=18 and there is no k>0 less than 10 with sigma(k)=18
%p N:= 1000: # to use values of sigma <= N
%p V:= Vector(N): A:= Vector(N):
%p for n from 1 to N do
%p v:= numtheory:-sigma(n);
%p if v <= N then
%p if V[v] = 0 then V[v]:= n
%p else A[n]:= V[v]
%p fi
%p fi
%p od:
%p subs(0=NULL, convert(A,list)); # _Robert Israel_, Mar 30 2018
%t Clear[tmp]; Function[n,If[Head[ #1]===tmp,#1=n;Unevaluated[Sequence[]],#1]& [tmp[DivisorSigma[1,n]]]]/@Range[200]
%Y Cf. A069822, A131903 - A131908.
%K easy,nonn
%O 1,1
%A Peter Pein (petsie(AT)dordos.net), Jul 26 2007