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A118363 Factorial base Niven (or Harshad) numbers: numbers that are divisible by the sum of their factorial base digits.

%I A118363 #37 Jan 05 2025 19:51:38
%S A118363 1,2,4,6,8,9,12,16,18,20,24,26,27,30,35,36,40,48,52,54,56,60,70,72,75,
%T A118363 80,90,91,96,105,108,112,117,120,122,123,126,132,135,140,144,148,150,
%U A118363 152,156,161,168,175,180,186,192,204,208,210,222,224,240,244,245,246
%N A118363 Factorial base Niven (or Harshad) numbers: numbers that are divisible by the sum of their factorial base digits.
%C A118363 Also called "Fiven" numbers [Dahlenberg and Edgar]. - _N. J. A. Sloane_, Jun 25 2018
%H A118363 Antti Karttunen, <a href="/A118363/b118363.txt">Table of n, a(n) for n = 1..10000</a>
%H A118363 Paul Dahlenberg and Tom Edgar, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/56-2/dalenberb011718.pdf">Consecutive factorial base Niven numbers</a>, The Fibonacci Quarterly, Vol. 56, No. 2 (2018), pp. 163-166.
%H A118363 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%e A118363 a(8) = 16 because it is written 220 in factorial base and 2 + 2 + 0 = 4, which is a divisor of 16.
%e A118363 17 is not on the list because it is written 221 in factorial base and 2 + 2 + 1 = 5, which is not a divisor of 17.
%t A118363 (*For the definition of the factorial base version of IntegerDigits, see A007623*) Select[Range[250],IntegerQ[ #/(Plus@@factBaseIntDs[ # ])]&]
%o A118363 (Scheme, with Antti Karttunen's IntSeq-library) (define A118363 (ZERO-POS 1 1 A286604)) ;; _Antti Karttunen_, Jun 18 2017
%o A118363 (Python)
%o A118363 def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p
%o A118363 def ok(n): return n%sum(map(int, list(str(a007623(n)))))==0
%o A118363 print([n for n in range(1, 251) if ok(n)]) # _Indranil Ghosh_, Jun 21 2017
%o A118363 (PARI) is(n) = {my(k = n, m = 2, r, s = 0); while([k, r] = divrem(k, m); k != 0 || r != 0, s += r; m++); !(n % s);} \\ _Amiram Eldar_, Oct 08 2024
%Y A118363 Cf. A007623 (integers written in factorial base), A005349 (base 10 Harshad numbers).
%Y A118363 Cf. A286607 (complement), A034968, A286590.
%Y A118363 Positions of zeros in A286604.
%K A118363 base,easy,nonn
%O A118363 1,2
%A A118363 _Alonso del Arte_, May 15 2006