A333499 Number of numbers the sum of whose digits' factorials equals n.

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

Author

Mateusz Winiarski, Mar 24 2020

Keywords

• nonn
• base

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.

Examples

			a(2)=3 because there are 3 numbers whose sum of factorials of the digits equals 2: 2, 10, 11.
		

Crossrefs

Cf. A002275, A061602.

Programs

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 *)

Extensions

More terms from Giovanni Resta, Mar 24 2020