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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
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1, 3, 6, 9, 12, 18, 54, 117, 272, 294, 296, 320, 783, 1125, 2088, 3375, 16164, 16407, 26286, 26777, 26784, 27516, 27568, 45945, 74970
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Most, but not all, of the terms in this sequence are divisible by 3; is this a coincidence?
In general, terms should be more likely to occur in regions where the number of digits in the sum of the first n factorials is close to an integer multiple of 2*n/9. This happens, e.g., around n = 268, 449, 752, 1257, 2100, 3506, 5851, 9763, 16290, 27177, 45337, 75631, 126165, etc. [From Jon E. Schoenfield (jonscho(AT)hiwaay.net), Jun 16 2010]
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EXAMPLE
| 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
| s = 0; Do[s += n!; k = Plus @@ IntegerDigits[s]; If[Mod[k, n] == 0, Print[n]], {n, 1, 10000}]
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CROSSREFS
| Sequence in context: A065119 A173195 A092421 * A175589 A203016 A153838
Adjacent sequences: A109654 A109655 A109656 * A109658 A109659 A109660
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KEYWORD
| base,more,nonn
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AUTHOR
| Ryan Propper (rpropper(AT)stanford.edu), Aug 06 2005
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EXTENSIONS
| More terms from Jon E. Schoenfield (jonscho(AT)hiwaay.net), Jun 16 2010
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