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A344487 a(n) is the least k such that n is divisible by the sum of digits of k and k is divisible by the sum of digits of n; a(n) = -1 if no such k exists.

%I A344487 #14 May 27 2021 12:31:30
%S A344487 1,2,3,4,5,6,7,8,9,1,10,3,76,10,12,35,296,9,10,2,3,20,10,6,14,184,9,
%T A344487 10,20999,3,100,10,12,98,16,9,10,11,12,4,10,6,99799,40,9,10,2099999,
%U A344487 12,52,5,12,49,1000,9,10,11,12,1001,7998998,6,7999999,200,9,10
%N A344487 a(n) is the least k such that n is divisible by the sum of digits of k and k is divisible by the sum of digits of n; a(n) = -1 if no such k exists.
%C A344487 Is a(n) > 0 for every n?
%H A344487 Rémy Sigrist, <a href="/A344487/b344487.txt">Table of n, a(n) for n = 1..500</a>
%H A344487 Rémy Sigrist, <a href="/A344487/a344487.gp.txt">PARI program for A344487</a>
%e A344487 For n = 15:
%e A344487 - the sum of digits of 15 is 6,
%e A344487 - so a(15) must be a multiple of 6,
%e A344487 - the sum of digits of 6 is 6, and 6 does not divide 15,
%e A344487 - the sum of digits of 12 is 3, and 3 divides 15,
%e A344487 - so a(15) = 12.
%o A344487 (PARI) See Links section.
%Y A344487 Cf. A005349, A007953, A344486.
%K A344487 nonn,base
%O A344487 1,2
%A A344487 _Rémy Sigrist_, May 21 2021