A333499 - OEIS

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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

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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.

LINKS

Table of n, a(n) for n=1..32.

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

Cf. A002275, A061602.

Sequence in context: A135364 A051291 A178178 * A257553 A143013 A113483

Adjacent sequences: A333496 A333497 A333498 * A333500 A333501 A333502

KEYWORD

nonn,base

AUTHOR

Mateusz Winiarski, Mar 24 2020

EXTENSIONS

More terms from Giovanni Resta, Mar 24 2020

STATUS

approved