%I #12 Jan 27 2022 21:12:55
%S 1,2,4,3,6,8,9,12,5,10,15,16,18,20,7,14,21,24,28,27,30,35,32,25,11,36,
%T 40,22,33,42,44,45,48,54,55,50,56,13,26,39,52,60,63,65,66,70,64,72,75,
%U 77,78,80,17,84,34,51,68,85,88,90,91,96,99,81,19,100,102
%N Smallest number not already in the sequence that is a divisor of A002182(n).
%e a(3) cannot be 3 because 3 is not a divisor of A002182(3)=4. a(4), however, can be 3 because 3 is a divisor of A002182(4)=6.
%t a[n_]:=a[n]=Min@Select[Divisors[max=t=k=0;While[t<n,k++;While[(d=DivisorSigma[0,k])<=max,k++];max=d;t++];k],FreeQ[Array[a,n-1],#]&];Array[a,30] (* _Giorgos Kalogeropoulos_, Jan 13 2022 *)
%Y Cf. A002182.
%K nonn
%O 1,2
%A _J. Lowell_, Jan 13 2022
%E More terms from _Amiram Eldar_, Jan 13 2022