%I #17 Mar 16 2023 12:13:37

%S 11,13,17,41,43,56,91,97,101,106,121,131,155,157,161,181,188,221,232,

%T 233,239,254,271,274,301,305,311,353,361,365,385,391,401,421,451,452,

%U 491,494,508,521,529,541,551,599,610,617,625,631,647,650,673,685,721

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

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

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

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

%H Paolo P. Lava, <a href="/A209871/b209871.txt">Table of n, a(n) for n = 1..10000</a>

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

%p with(numtheory);

%p A209871:=proc(i)

%p local a,b,n;

%p for n from 1 to i do

%p a:=n; b:=0;

%p while a>0 do b:=b+(a mod 10); a:=trunc(a/10); od;

%p a:=n mod b; if a=1 then print(n); fi;

%p od; end:

%p A209871(10000);

%o (Magma) [n: n in [1..721] | n mod s eq 1 where s is &+Intseq(n)]; // _Bruno Berselli_, Mar 29 2012

%Y Cf. A005349.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Mar 29 2012