

A109657


Numbers n such that the sum of the digits of Sum_{k=1..n}(k!) is divisible by n.


0



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
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OFFSET

1,2


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.  Jon E. Schoenfield, Jun 16 2010


LINKS

Table of n, a(n) for n=1..25.


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.


MATHEMATICA

s = 0; Do[s += n!; k = Plus @@ IntegerDigits[s]; If[Mod[k, n] == 0, Print[n]], {n, 1, 10000}]


CROSSREFS

Sequence in context: A173195 A232920 A092421 * A175589 A282759 A203016
Adjacent sequences: A109654 A109655 A109656 * A109658 A109659 A109660


KEYWORD

base,more,nonn


AUTHOR

Ryan Propper, Aug 06 2005


EXTENSIONS

More terms from Jon E. Schoenfield, Jun 16 2010


STATUS

approved



