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Search: id:A109657
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| A109657 |
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Numbers n such that the sum of the digits of sum_{k=1..n}(k!) is divisible by n. |
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+0
1
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| 1, 3, 6, 9, 12, 18, 54, 117, 272, 294, 296, 320, 783, 1125, 2088, 3375
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Next term after 3375 is greater than 10000. Most, but not all, of the terms in this sequence are divisible by 3; is this a coincidence?
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EXAMPLE
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sum_{k=1..12}(k!) = 522956313; the digits of 522956313 sum to 36, which is divisible by 12, so 12 is in the sequence.
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MATHEMATICA
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s = 0; Do[s += 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: A063996 A065119 A092421 this_sequence A118519 A089757 A083491
Adjacent sequences: A109654 A109655 A109656 this_sequence A109658 A109659 A109660
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KEYWORD
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base,more,nonn
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AUTHOR
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Ryan Propper (rpropper(AT)stanford.edu), Aug 06 2005
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