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A354854
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Smallest number of powers of n with positive exponents that sum to a factorial.
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1
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1, 1, 2, 3, 8, 1, 12, 3, 16, 3, 30, 2, 48, 20, 6, 15, 80, 6, 108, 6, 20, 63, 176, 1, 24, 50, 50, 18
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OFFSET
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1,3
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COMMENTS
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For n > 1, a(n) is the smallest base-n digit sum of m! for m >= A002034(n). Values m = A002034(n) correspond to A354861, and so a(n) <= A354861(n). The two sequences share many terms but differ: a(14) = 20 < 22 = A354861(14).
The sequence likely continues as 280, 4, 330, ...
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LINKS
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EXAMPLE
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a(7) = 12 since 7! = 2*7^4 + 4*7^2 + 6*7^1 with 2+4+6=12, and the sum of 11 or less powers of 7 cannot be a multiple of 48.
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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