A209871 Quasi-Niven (or Quasi-Harshad) numbers: numbers that divided by the sum of their digits leave 1 as remainder.

11, 13, 17, 41, 43, 56, 91, 97, 101, 106, 121, 131, 155, 157, 161, 181, 188, 221, 232, 233, 239, 254, 271, 274, 301, 305, 311, 353, 361, 365, 385, 391, 401, 421, 451, 452, 491, 494, 508, 521, 529, 541, 551, 599, 610, 617, 625, 631, 647, 650, 673, 685, 721

Offset: 1

Author

Paolo P. Lava, Mar 29 2012

Keywords

• nonn
• base

Comments

Numbers n for which [n mod s(n)]=1, where s(n) is the sum of the digits of n.

z-Niven numbers with A=1 and B=-1 (see comment in A005349).

First pair of consecutive numbers is {232,233}.

Examples

			s(43)=7 and 6*7+1=43.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005349.

Programs

Magma

[n: n in [1..721] | n mod s eq 1 where s is &+Intseq(n)]; // Bruno Berselli, Mar 29 2012

Maple

with(numtheory);
A209871:=proc(i)
local a,b,n;
for n from 1 to i do
  a:=n; b:=0;
  while a>0 do b:=b+(a mod 10); a:=trunc(a/10); od;
  a:=n mod b; if a=1 then print(n); fi;
od; end:
A209871(10000);