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

Author

Alonso del Arte, May 15 2006

Keywords

• base
• easy
• nonn

Comments

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

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Paul Dahlenberg and Tom Edgar, Consecutive factorial base Niven numbers, The Fibonacci Quarterly, Vol. 56, No. 2 (2018), pp. 163-166.
• Index entries for sequences related to factorial base representation.

Crossrefs

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

Cf. A286607 (complement), A034968, A286590.

Positions of zeros in A286604.

Programs

Mathematica

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

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

Python

def a007623(n, p=2): return n if n
Indranil Ghosh, Jun 21 2017