

A118363


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


8



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, 80, 90, 91, 96, 105, 108, 112, 117, 120, 122, 123, 126, 132, 135, 140, 144, 148, 150, 152, 156, 161, 168, 175, 180, 186, 192, 204, 208, 210, 222, 224, 240, 244, 245, 246
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OFFSET

1,2


COMMENTS

Also called "Fiven" numbers [Dahlenberg and Edgar].  N. J. A. Sloane, Jun 25 2018


REFERENCES

Paul Dahlenberg and T. Edgar, Consecutive factorial base Niven numbers, Fib. Q., 56:2 (2018), 163166.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences related to factorial base representation


EXAMPLE

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


MATHEMATICA

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


PROG

(Scheme, with Antti Karttunen's IntSeqlibrary) (define A118363 (ZEROPOS 1 1 A286604)) ;; Antti Karttunen, Jun 18 2017
(Python)
def a007623(n, p=2): return n if n<p else a007623(int(n/p), p+1)*10 + n%p
def ok(n): return 1 if n%sum(map(int, list(str(a007623(n)))))==0 else 0
print [n for n in xrange(1, 251) if ok(n)] # Indranil Ghosh, Jun 21 2017


CROSSREFS

Cf. A007623 (Integers written in factorial base), A005349 (Base 10 Harshad numbers).
Cf. A286607 (complement), A286590.
Positions of zeros in A286604.
Sequence in context: A241562 A100345 A261011 * A146982 A298305 A090958
Adjacent sequences: A118360 A118361 A118362 * A118364 A118365 A118366


KEYWORD

base,easy,nonn


AUTHOR

Alonso del Arte, May 15 2006


STATUS

approved



