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A349403
Sum of the digits of Sum_{k=1..n} k!.
1
0, 1, 3, 9, 6, 9, 18, 18, 18, 18, 27, 36, 36, 54, 54, 36, 45, 45, 72, 72, 63, 81, 99, 99, 117, 108, 99, 126, 126, 144, 117, 162, 144, 153, 171, 171, 153, 180, 180, 198, 171, 225, 207, 252, 225, 261, 261, 252, 270, 234, 270, 261, 279, 324, 324, 306, 342, 333, 333, 297, 351, 360, 351, 333, 387, 405, 369
OFFSET
0,3
COMMENTS
If n > 4, then 9 divides a(n).
FORMULA
a(n) = A007953(A007489(n)).
a(n) = A127554(n+1) - 1 for n > 3.
EXAMPLE
n | A007489 | A003422 | a(n) | A127554 |
-----+----------+---------+------+---------+
0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 |
2 | 3 | 2 | 3 | 2 |
3 | 9 | 4 | 9 | 4 |
4 | 33 | 10 | 6 | 1 |
5 | 153 | 34 | 9 | 7 |
6 | 873 | 154 | 18 | 10 |
7 | 5913 | 874 | 18 | 19 |
8 | 46233 | 5914 | 18 | 19 |
9 | 409113 | 46234 | 18 | 19 |
10 | 4037913 | 409114 | 27 | 19 |
11 | 43954713 | 4037914 | 36 | 28 |
MATHEMATICA
Table[Total[IntegerDigits[Sum[k!, {k, n}]]], {n, 0, 66}] (* Stefano Spezia, Nov 16 2021 *)
PROG
(PARI) a(n) = sumdigits(sum(k=1, n, k!));
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Seiichi Manyama, Nov 15 2021
STATUS
approved