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 A004152 Sum of digits of n!. 18
 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 EXAMPLE a(5) = 3 because 5! = 120 and 1 + 2 + 0 = 3. a(6) = 9 because 6! = 720 and 7 + 2 + 0 = 9. MAPLE P:=proc(n) local i, t1, t2; for i from 0 by 1 to n do t1:=i!; t2:=0; while t1 <> 0 do t2:= t2+(t1 mod 10); t1 := floor(t1/10); od; print(t2); od; end: P(100); # Paolo P. Lava, Jun 30 2006 # Simpler alternative: 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 Adjacent sequences:  A004149 A004150 A004151 * A004153 A004154 A004155 KEYWORD nonn,base AUTHOR STATUS approved

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)