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 A333499 #21 May 31 2022 12:53:29
%S A333499 2,3,7,17,41,100,242,587,1423,3450,8364,20278,49162,119189,288963,
%T A333499 700565,1698457,4117757,9983133,24203212,58678520,142260817,344898611,
%U A333499 836175797,2027233339,4914845690,11915603246,28888313016,70037127930,169798744773,411661851057,998037293164
%N A333499 Number of numbers the sum of whose digits' factorials equals n.
%C A333499 Also number of occurrences of n in A061602.
%C A333499 All numbers whose sum of digits' factorials equals n are less than or equal to R_n (A002275).
%C A333499 10^n has sum of factorial of the digits equal to n, so all terms are greater than zero.
%e A333499 a(2)=3 because there are 3 numbers whose sum of factorials of the digits equals 2: 2, 10, 11.
%t A333499 permC[w_] := Length[w]!/Times @@ ((Last /@ Tally[w])!); a[1]=2; a[n_] := Block[{s = 0, w, f = {1}}, While[Last[f] < n, AppendTo[f, Last[f] (Length[f] + 1)]]; Do[ p = IntegerPartitions[k, {1, k}, f]; Do[ If[k == n, s += permC[q], w = Join[q, 0 Range[n - k]]; s += permC[w] - permC[Most[w]]], {q, p}], {k, n}]; s]; Array[a, 32] (* _Giovanni Resta_, Mar 24 2020 *)
%Y A333499 Cf. A002275, A061602.
%K A333499 nonn,base
%O A333499 1,1
%A A333499 _Mateusz Winiarski_, Mar 24 2020
%E A333499 More terms from _Giovanni Resta_, Mar 24 2020