

A114440


Numbers which divided by the sum of their digits (Harshad or Niven numbers) give integers which are also divided by the sum of their digits (until a single digit Harshad remains).


7



1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 18, 21, 24, 27, 36, 42, 45, 48, 54, 63, 72, 81, 84, 108, 162, 216, 243, 324, 378, 405, 432, 486, 648, 756, 864, 972, 1296, 1458, 1944, 2916, 3402, 4374, 5832, 6804, 7290, 8748, 11664, 13122, 13608, 15552, 17496, 23328, 26244
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

The sequence is finite with a(15095), a 1434digit number, being the final term.  Hans Havermann and Ray Chandler, Jan 21 2014


LINKS

Donovan Johnson, Table of n, a(n) for n = 1..235 (terms < 10^17)
Hans Havermann and Ray Chandler, Table of n, a(n) for n = 1..15095 (9.3 MB file)
Kornel, Ojciec i Syn.


EXAMPLE

The number 216 is a term of the sequence because it is divisible by the sum of its digits: 2+1+6=9; 216/9=24. Also, the successive quotients are divisible by the sum of their digits, until a single digit Harshad remains: 24: 2+4=6; 24/6=4 and 4: 4/4=1.


MATHEMATICA

s=w={1}; Do[t={}; Do[v=s[[k]]; u={}; Do[If[Total[IntegerDigits[c*v]]==c, AppendTo[u, c*v]], {c, 2, 7000}]; t=Join[t, u], {k, Length[s]}]; s=Sort[t]; w=Join[w, s], {440}]; Union[w] (* Hans Havermann, Jan 21 2014 *)


PROG

(PARI) v=vector(118); for(n=1, 9, v[n]=n; print1(n ", ")); c=9; for(n=10, 10^9, d=length(Str(n)); m=n; s=0; for(j=1, d, s=s+m%10; m=m\10); if(s==1, next); if(n%s==0, m=n/s, next); forstep(j=c, 1, 1, if(v[j]<=m, if(v[j]==m, c++; v[c]=n; print1(n ", ")); next(2)))) /* Donovan Johnson, Apr 09 2013 */


CROSSREFS

Cf. A005349, A097569, A235600, A235601, A236295, A236362, A236363, A236385.
Sequence in context: A079238 A079042 A193455 * A217973 A097518 A097569
Adjacent sequences: A114437 A114438 A114439 * A114441 A114442 A114443


KEYWORD

nonn,base,fini,full


AUTHOR

Piotr K. Olszewski (piotrkornelolszewski(AT)poczta.onet.pl), Feb 14 2006


EXTENSIONS

Offset corrected by Donovan Johnson, Apr 09 2013
a(54)a(235) from Donovan Johnson, Apr 09 2013
a(236)a(15095) from Hans Havermann and Ray Chandler, Jan 21 2014


STATUS

approved



