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

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

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), 163-166.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Paul Dahlenberg and T. Edgar, Consecutive factorial base Niven numbers, preprint.

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 IntSeq-library) (define A118363 (ZERO-POS 1 1 A286604)) ;; Antti Karttunen, Jun 18 2017
(Python)
def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p
def ok(n): return n%sum(map(int, list(str(a007623(n)))))==0
print([n for n in range(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: A261011 A354360 A333426 * A337674 A324521 A146982

Adjacent sequences: A118360 A118361 A118362 * A118364 A118365 A118366

Keyword

base,easy,nonn

Author

Alonso del Arte, May 15 2006

Status

approved