TITLE: A factorian is a number equal to the sum of the factorials of its digits, e.g., 145 = 1! + 4! + 5! and 40,585 = 4! + 0! + 5! + 8! + 5!. Let F be the largest factorian. Here I provide a very simple proof that F < 2,000,000.
AUTHOR: @games_to_change
#QUARK
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So what’s the largest “Factorian”?
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There are only 4 factorian: 1! 2! 145! 40585!
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Nice argument, even if there's a minor mistake (9! × 7 wasn't exact, but the argument stays the same...) What if we change base? It could be interesting for a larger base than 10 especially
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for F < 2.000.000 fmax is 1!+9!*6= 2.177.281 -> 1!+8!+9!*5= 1.854.721 -> 1!+8!+8!+9!*4 = 1.532.161 -> 1!+5!+9!*5 = 1.814.521 -> 1!+5!+8!+9!*4= 1.491.961 so F can't be between 1.500.000 and 2.000.000
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