%I #36 Oct 08 2024 18:38:43

%S 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 80,90,91,96,105,108,112,117,120,122,123,126,132,135,140,144,148,150,

%U 152,156,161,168,175,180,186,192,204,208,210,222,224,240,244,245,246

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

%C Also called "Fiven" numbers [Dahlenberg and Edgar]. - _N. J. A. Sloane_, Jun 25 2018

%H Antti Karttunen, <a href="/A118363/b118363.txt">Table of n, a(n) for n = 1..10000</a>

%H Paul Dahlenberg and Tom Edgar, <a href="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 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.

%e a(8) = 16 because it is written 220 in factorial base and 2 + 2 + 0 = 4, which is a divisor of 16.

%e 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 (*For the definition of the factorial base version of IntegerDigits, see A007623*) Select[Range[250],IntegerQ[ #/(Plus@@factBaseIntDs[ # ])]&]

%o (Scheme, with Antti Karttunen's IntSeq-library) (define A118363 (ZERO-POS 1 1 A286604)) ;; _Antti Karttunen_, Jun 18 2017

%o (Python)

%o def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p

%o def ok(n): return n%sum(map(int, list(str(a007623(n)))))==0

%o print([n for n in range(1, 251) if ok(n)]) # _Indranil Ghosh_, Jun 21 2017

%o (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 Cf. A007623 (integers written in factorial base), A005349 (base 10 Harshad numbers).

%Y Cf. A286607 (complement), A034968, A286590.

%Y Positions of zeros in A286604.

%K base,easy,nonn

%O 1,2

%A _Alonso del Arte_, May 15 2006