A004152 Sum of digits of n!.
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
Offset: 0
Examples
a(5) = 3 because 5! = 120 and 1 + 2 + 0 = 3. a(6) = 9 because 6! = 720 and 7 + 2 + 0 = 9.
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.
Crossrefs
Programs
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Magma
[&+Intseq(Factorial(n)): n in [0..70]]; // Vincenzo Librandi, Jan 30 2015
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Maple
seq(convert(convert(n!,base,10),`+`),n=0..100); # Robert Israel, Nov 13 2014
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Mathematica
Table[ Plus @@ IntegerDigits[n!], {n, 0, 100}] (* Enrique Pérez Herrero, Mar 01 2009 *) -
PARI
a(n)=my(v=eval(Vec(Str(n!))));sum(i=1,#v,v[i]) \\ Charles R Greathouse IV, Dec 27 2011
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PARI
a(n) = sumdigits(n!); \\ Michel Marcus, Sep 18 2014
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
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
Comments