

A118363


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


30



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



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

(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).


KEYWORD

base,easy,nonn


AUTHOR



STATUS

approved



