This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A334816 #6 May 12 2020 13:00:17
%S A334816 1,2,3,5,9,17,43,137,281,673,2401,4801,9601,170761,341521,683041,
%T A334816 5114881,31846081,131955841,1985902081,7545868801
%N A334816 Least number that reaches 1 after n iterations of the map k -> usigma(k)/ud(k) if ud(k) | usigma(k), and k -> 1 otherwise, where ud(k) is the number of unitary divisors of k (A034444) and usigma(k) is their sum (A034448).
%C A334816 Apparently, all the terms are primes or powers of primes.
%C A334816 a(21) > 10^10, if it exists.
%e A334816 a(3) = 5 since usigma(5)/ud(5) = 6/2 = 3, usigma(3)/ud(3) = 4/2 = 2, and usigma(2)/ud(2) = 3/2 is not an integer, hence there are 3 iterations: 5 -> 3 -> 2 -> 1, and 5 is the least number with 3 iterations.
%t A334816 usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); ud[n_] := 2^PrimeNu[n]; rat[n_] := If[IntegerQ[r = usigma[n]/ud[n]], r, 1]; f[n_] := Length @ FixedPointList[rat, n] - 1; max = 10; seq = Table[0, {max}]; c = 0; n = 1; While[c < max, i = f[n]; If[i <= max && seq[[i]] == 0, c++; seq[[i]] = n]; n++]; seq
%Y A334816 Cf. A034444, A034448, A103826, A103827, A330814, A330815.
%K A334816 nonn,more
%O A334816 0,2
%A A334816 _Amiram Eldar_, May 12 2020