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%I #15 Oct 19 2021 10:57:41
%S 3,2,7,1,6,5,5,4,4,4,3,3,2,3,1,1,3,2,2,1,1,3,3,1,2,2,1,1,3,1,2,1,1,3,
%T 2,1,2,2,1,2,3,1,2,3,1,3,3,1,2,2,2,1,2,1,1,1,1,3,3,6,2,2,1,1,2,1,2,1,
%U 1,2,3,5,2,2,1,1,2,1,2,2,1,3,2,4,1,2,5,4,5,1,4,4,1,4,3,3,3,3,2,1
%N For n >= 1; x = n, then iterate x --> x + d(x) until d(x + d(x)) >= d(x). a(n) gives the number of iteration steps where d(i) is the number of divisors of i, A000005(i).
%C a(n) = 1 for n from A260577.
%e n = 1; x(1) = 1 + d(1) = 2, d(1 + d(1)) >= d(1) thus x(2) = 2 + d(2) = 4, d(2 + d(2)) >= d(2) thus x(3) = 4 + d(4) = 7, d(4 + d(4)) < d(4), stop. a(1) = 3.
%t d[n_] := DivisorSigma[0, n]; x[n_] := n + d[n]; a[n_] := Length@ NestWhileList[x, n, d[#] <= d[x[#]] &]; Array[a, 100] (* _Amiram Eldar_, Oct 15 2021 *)
%Y Cf. A000005, A062249, A175304, A259934, A260577, A286529.
%K nonn
%O 1,1
%A _Ctibor O. Zizka_, Oct 13 2021