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A109662
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Numbers n such that the sum of the digits of (n^n - n!) is divisible by n.
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0
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1, 2, 3, 9, 14, 15, 29, 33, 45, 81, 102, 105, 126, 142, 157, 288, 414, 1184, 2133, 10449, 16369, 17221, 46524, 214179, 216741
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OFFSET
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1,2
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COMMENTS
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The quotients are: 0, 1, 1, 5, 5, 6, 7, 6, 8, 9, 9, 9, 9, 10, 10, 11, 12, 14, 15, 18, 19, 19, 21, 24, 24.
No more terms < 500000. [Lars Blomberg, Jul 05 2011]
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LINKS
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Table of n, a(n) for n=1..25.
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EXAMPLE
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The digits of 414^414 - 414! sum to 4968 and 4968 is divisible by 414, so 414 is in the sequence.
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MATHEMATICA
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Do[s = n^n - n!; k = Plus @@ IntegerDigits[s]; If[Mod[k, n] == 0, Print[n]], {n, 1, 10000}]
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CROSSREFS
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Sequence in context: A269154 A225792 A057293 * A116222 A048038 A113501
Adjacent sequences: A109659 A109660 A109661 * A109663 A109664 A109665
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KEYWORD
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base,more,nonn
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AUTHOR
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Ryan Propper, Aug 06 2005
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EXTENSIONS
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Terms a(20)-a(25) from Lars Blomberg, Jul 05 2011.
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STATUS
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approved
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