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%I #24 Nov 19 2021 07:26:20
%S 0,1,3,9,6,9,18,18,18,18,27,36,36,54,54,36,45,45,72,72,63,81,99,99,
%T 117,108,99,126,126,144,117,162,144,153,171,171,153,180,180,198,171,
%U 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
%N Sum of the digits of Sum_{k=1..n} k!.
%C If n > 4, then 9 divides a(n).
%F a(n) = A007953(A007489(n)).
%F a(n) = A127554(n+1) - 1 for n > 3.
%e n | A007489 | A003422 | a(n) | A127554 |
%e -----+----------+---------+------+---------+
%e 0 | 0 | 0 | 0 | 0 |
%e 1 | 1 | 1 | 1 | 1 |
%e 2 | 3 | 2 | 3 | 2 |
%e 3 | 9 | 4 | 9 | 4 |
%e 4 | 33 | 10 | 6 | 1 |
%e 5 | 153 | 34 | 9 | 7 |
%e 6 | 873 | 154 | 18 | 10 |
%e 7 | 5913 | 874 | 18 | 19 |
%e 8 | 46233 | 5914 | 18 | 19 |
%e 9 | 409113 | 46234 | 18 | 19 |
%e 10 | 4037913 | 409114 | 27 | 19 |
%e 11 | 43954713 | 4037914 | 36 | 28 |
%t Table[Total[IntegerDigits[Sum[k!,{k,n}]]],{n,0,66}] (* _Stefano Spezia_, Nov 16 2021 *)
%o (PARI) a(n) = sumdigits(sum(k=1, n, k!));
%Y Cf. A004152, A007489, A007953, A127554.
%K nonn,base
%O 0,3
%A _Seiichi Manyama_, Nov 15 2021
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