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A004152 Sum of digits of n!. 23
1, 1, 2, 6, 6, 3, 9, 9, 9, 27, 27, 36, 27, 27, 45, 45, 63, 63, 54, 45, 54, 63, 72, 99, 81, 72, 81, 108, 90, 126, 117, 135, 108, 144, 144, 144, 171, 153, 108, 189, 189, 144, 189, 180, 216, 207, 216, 225, 234, 225, 216, 198, 279, 279, 261, 279, 333, 270, 288 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
If n > 5, then 9 divides a(n). - Enrique Pérez Herrero, Mar 01 2009
LINKS
Maciej Ireneusz Wilczynski, Table of n, a(n) for n = 0..10000
Florian Luca, The number of non-zero digits of n!, Canad. Math. Bull. 45 (2002), pp. 115-118.
Carlo Sanna, On the sum of digits of the factorial, Journal of Number Theory 147 (February 2015), pp. 836-841. arXiv:1409.4912 [math.NT].
Carlo Sanna, On the sum of digits of the factorial, Journal of Number Theory 147 (February 2015), pp. 836-841.
FORMULA
Luca shows that a(n) >> log n. In particular, a(n) > log_10 n - log_10 log_10 n. - Charles R Greathouse IV, Dec 27 2011
a(n) < floor(log_10(n)*9/2). - Carmine Suriano, Feb 20 2013
a(n) = A007953(A000142(n)). - Michel Marcus, Sep 18 2014
a(n) < 9*(A034886(n) - A027868(n)). - Enrique Pérez Herrero, Nov 16 2014
Sanna improved Luca's result to a(n) >> log n log log log n. - Charles R Greathouse IV, Jan 30 2015
a(n) = 9*A202708(n), n>=6. - R. J. Mathar, Jul 30 2021
EXAMPLE
a(5) = 3 because 5! = 120 and 1 + 2 + 0 = 3.
a(6) = 9 because 6! = 720 and 7 + 2 + 0 = 9.
MAPLE
seq(convert(convert(n!, base, 10), `+`), n=0..100); # Robert Israel, Nov 13 2014
MATHEMATICA
Table[ Plus @@ IntegerDigits[n!], {n, 0, 100}] (* Enrique Pérez Herrero, Mar 01 2009 *)
PROG
(PARI) a(n)=my(v=eval(Vec(Str(n!)))); sum(i=1, #v, v[i]) \\ Charles R Greathouse IV, Dec 27 2011
(PARI) a(n) = sumdigits(n!); \\ Michel Marcus, Sep 18 2014
(Magma) [&+Intseq(Factorial(n)): n in [0..70]]; // Vincenzo Librandi, Jan 30 2015
CROSSREFS
Cf. A000142 (factorial), A007953 (sum of digits), A079584 (same in base 2), A086358 (digital root of n!).
Sequence in context: A105815 A136696 A086358 * A071678 A316164 A319276
KEYWORD
nonn,base
AUTHOR
STATUS
approved

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Last modified February 27 21:03 EST 2024. Contains 370378 sequences. (Running on oeis4.)