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 A380435 #10 Jan 25 2025 12:39:49
%S A380435 1,2,2,2,2,2,2,2,2,1,11,12,12,12,12,12,12,12,12,2,21,22,22,22,22,22,
%T A380435 22,22,22,2,21,22,22,22,22,22,22,22,22,2,21,22,22,22,22,22,22,22,22,2,
%U A380435 21,22,22,22,22,22,22,22,22,2,21,22,22,22,22,22,22,22,22,2,21,22,22,22,22,22
%N A380435 Erase digit 0 from decimal expansion of n. Then repeatedly apply the number of divisor function (A000005) onto each digit until a stationary value is reached. a(n) is the final stationary value (if it is reached for all digits).
%C A380435 The number of iterations is 0, 1, 2, 3 for numbers containing the highest digits (1, 2), (3,5,7), (4, 9), (6, 8). n >= a(n) >= 1.
%F A380435 a(A007931(n)) = A007931(n).
%F A380435 For r = 1, k >= 0:
%F A380435 a(10^k) = 1
%F A380435 a((10^k - 1)/9) = (10^k - 1)/9.
%F A380435 For r from [2, 9], k >= 0:
%F A380435 a(r*10^k) = 2.
%F A380435 a(r*(10^k - 1)/9) = 2*(10^k - 1)/9.
%e A380435 For n = 21 a(21) = 21.
%e A380435 For n = 408 we iterate 48 --> 34 --> 23 --> 22, thus, after 3 iterations, a(408) = 22.
%t A380435 a[n_] := FromDigits[IntegerDigits[n] /. {0 -> Nothing, _?(# > 1 &) -> 2}]; Array[a, 100] (* _Amiram Eldar_, Jan 24 2025 *)
%Y A380435 Cf. A002275, A002276 - A002283, A004719, A007931, A111066.
%K A380435 nonn,base
%O A380435 1,2
%A A380435 _Ctibor O. Zizka_, Jan 24 2025