|
| |
|
|
A005349
|
|
Niven (or Harshad) numbers: numbers that are divisible by the sum of their digits.
(Formerly M0481)
|
|
122
|
|
|
|
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 102, 108, 110, 111, 112, 114, 117, 120, 126, 132, 133, 135, 140, 144, 150, 152, 153, 156, 162, 171, 180, 190, 192, 195, 198, 200, 201, 204
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
z-Niven numbers are numbers n which are divisible by (A*s(n)+ B) where A,B are integers and s(n) is sum of digits of n. Niven numbers have A=1, B=0. - Ctibor O. ZIZKA (ctibor.zizka(AT)seznam.cz), Feb 23 2008
A070635(a(n)) = 0. A038186 is a subsequence. - Reinhard Zumkeller, Mar 10 2008
A049445 is a subsequence of this sequence. [Ctibor O. Zizka, Sep 06 2010]
Complement of A065877; A188641(a(n)) = 1; A070635(a(n)) = 0. [Reinhard Zumkeller, Apr 07 2011]
A001101, the Moran numbers, are a subsequence. - Reinhard Zumkeller, Jun 16 2011
A140866 gives the number of terms less or equal to 10^k. - Robert G. Wilson v, Oct 16 2012
|
|
|
REFERENCES
|
R. K. Guy, The second strong law of small numbers. Math. Mag. 63 (1990), no. 1, 3-20.
R. E. Kennedy and C. N. Cooper, On the natural density of the Niven numbers, Abstract 816-11-219, Abstracts Amer. Math. Soc., 6 (1985), 17.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 171.
|
|
|
LINKS
|
N. J. A. Sloane, Table of n, a(n) for n = 1..11872 (all a(n) <= 100000)
Jean-Marie De Koninck and Nicolas Doyon, Large and Small Gaps Between Consecutive Niven Numbers, J. Integer Seqs., Vol. 6, 2003.
R. E. Kennedy, Niven Numbers for Fun and Profit
G. Villemin's Almanac of Numbers, Nombres de Harshad
Eric Weisstein's World of Mathematics, Harshad Numbers
Eric Weisstein's World of Mathematics, Digit
Wikipedia, Harshad number
|
|
|
EXAMPLE
|
195 is a term of the sequence because it is divisible by 15 (=1+9+5).
|
|
|
MAPLE
|
s:=proc(n) local N:N:=convert(n, base, 10):sum(N[j], j=1..nops(N)) end:p:=proc(n) if floor(n/s(n))=n/s(n) then n else fi end: seq(p(n), n=1..210); (Deutsch)
|
|
|
MATHEMATICA
|
fQ[n_] := Mod[n, Plus @@ IntegerDigits@ n] == 0; Select[ Range[1000], fQ] (* Alonso del Arte, Aug 04 2004 and modified by Robert G. Wilson v, Oct 16 2012 *)
|
|
|
PROG
|
(Haskell)
a005349 n = a005349_list !! (n-1)
a005349_list = filter ((== 0) . a070635) [1..]
-- Reinhard Zumkeller, Aug 17 2011, Apr 07 2011
(MAGMA) [ n: n in [1..204] | n mod (&+Intseq(n)) eq 0 ]; // Bruno Berselli, May 28 2011
(PARI) is(n)=n%sumdigits(n)==0 \\ Charles R Greathouse IV, Oct 16 2012
|
|
|
CROSSREFS
|
Cf. A007953, A052018, A052019, A052020, A052021, A052022, A028834, A001101, A038186, A049445, A065877, A070635, A188641.
A001102 is a subsequence.
Sequence in context: A143289 A064807 A007603 * A225780 A225782 A085135
Adjacent sequences: A005346 A005347 A005348 * A005350 A005351 A005352
|
|
|
KEYWORD
|
nonn,base,nice,easy
|
|
|
AUTHOR
|
N. J. A. Sloane, Robert G. Wilson v
|
|
|
STATUS
|
approved
|
| |
|
|
