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A333499
Number of numbers the sum of whose digits' factorials equals n.
0
2, 3, 7, 17, 41, 100, 242, 587, 1423, 3450, 8364, 20278, 49162, 119189, 288963, 700565, 1698457, 4117757, 9983133, 24203212, 58678520, 142260817, 344898611, 836175797, 2027233339, 4914845690, 11915603246, 28888313016, 70037127930, 169798744773, 411661851057, 998037293164
OFFSET
1,1
COMMENTS
Also number of occurrences of n in A061602.
All numbers whose sum of digits' factorials equals n are less than or equal to R_n (A002275).
10^n has sum of factorial of the digits equal to n, so all terms are greater than zero.
EXAMPLE
a(2)=3 because there are 3 numbers whose sum of factorials of the digits equals 2: 2, 10, 11.
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A135364 A051291 A178178 * A257553 A143013 A113483
KEYWORD
nonn,base
AUTHOR
Mateusz Winiarski, Mar 24 2020
EXTENSIONS
More terms from Giovanni Resta, Mar 24 2020
STATUS
approved