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A209871
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Quasi-Niven (or Quasi-Harshad) numbers: numbers that divided by the sum of their digits leave 1 as remainder.
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24
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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
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OFFSET
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1,1
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COMMENTS
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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}.
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LINKS
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EXAMPLE
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s(43)=7 and 6*7+1=43.
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MAPLE
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with(numtheory);
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:
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PROG
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(Magma) [n: n in [1..721] | n mod s eq 1 where s is &+Intseq(n)]; // Bruno Berselli, Mar 29 2012
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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