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A118363
Factorial base Niven (or Harshad) numbers: numbers that are divisible by the sum of their factorial base digits.
37
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
LINKS
Paul Dahlenberg and Tom Edgar, Consecutive factorial base Niven numbers, The Fibonacci Quarterly, Vol. 56, No. 2 (2018), pp. 163-166.
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
(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
CROSSREFS
Cf. A007623 (integers written in factorial base), A005349 (base 10 Harshad numbers).
Cf. A286607 (complement), A034968, A286590.
Positions of zeros in A286604.
Sequence in context: A261011 A354360 A333426 * A337674 A324521 A146982
KEYWORD
base,easy,nonn
AUTHOR
Alonso del Arte, May 15 2006
STATUS
approved