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A066419 Numbers k such that k! is not divisible by the sum of the decimal digits of k!.

%I A066419 #35 Sep 17 2024 15:45:49
%S A066419 432,444,453,458,474,476,485,489,498,507,509,532,539,541,548,550,552,
%T A066419 554,555,556,560,565,567,576,593,597,603,608,609,610,611,612,613,624,
%U A066419 630,632,634,640,645,657,663,665,683,685,686,692,698,703,706,708,714
%N A066419 Numbers k such that k! is not divisible by the sum of the decimal digits of k!.
%H A066419 Michael S. Branicky, <a href="/A066419/b066419.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Matthew Conroy)
%H A066419 Dimitri Zucker, <a href="https://www.youtube.com/watch?v=b2zhTrggRDE">Factorial Fact Frenzy (!)</a>, Combo Class Youtube video (2022).
%e A066419 The sum of the decimal digits of 5! is 1+2+0=3 and 3 divides 120, so 5 is not in the sequence.
%e A066419 The sum of the decimal digits of 432! is 3897 = (9)(433) and 3897 does not divide 432!, so 432 is in the sequence.
%t A066419 Select[Range[1000], !Divisible[Factorial[#],Total[IntegerDigits[Factorial[#]]]] &], (* _Tanya Khovanova_, Jun 13 2021 *)
%o A066419 (Python)
%o A066419 from math import factorial
%o A066419 def sd(n): return sum(map(int, str(n)))
%o A066419 def ok(f): return f%sd(f) != 0
%o A066419 print([n for n in range(1, 715) if ok(factorial(n))]) # _Michael S. Branicky_, Jun 13 2021
%o A066419 (PARI) isA066419(n) = (Mod(n!, sumdigits(n!)) != 0) \\ _Jianing Song_, Aug 26 2024
%Y A066419 Cf. A004152 (sum of digits of n!).
%K A066419 base,easy,nonn
%O A066419 1,1
%A A066419 _Matthew Conroy_, Dec 25 2001