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Digital root of concatenation of all divisors of n (A037278).
5

%I #12 Sep 13 2014 11:16:40

%S 1,3,4,7,6,3,8,6,4,9,3,1,5,6,6,4,9,3,2,6,5,9,6,6,4,6,4,2,3,9,5,9,3,9,

%T 3,1,2,6,2,9,6,6,8,3,6,9,3,7,3,3,9,8,9,3,9,3,8,9,6,6,8,6,5,1,3,9,5,9,

%U 6,9,9,6,2,6,7,5,6,6,8,6,4,9,3,8,9,6,3,9,9,9,4,6,2,9,3,9,8,9,3,1,3,9,5,3,3

%N Digital root of concatenation of all divisors of n (A037278).

%C Also digital root of A034690 (sum of digits of all the divisors of n).

%C Also digital root of A000203 (sum of divisors of n). - _Michel Marcus_, Sep 13 2014

%H Nathaniel Johnston, <a href="/A190998/b190998.txt">Table of n, a(n) for n = 1..10000</a>

%e For n = 12: 1 + 2 + 3 + 4 + 6 + 1 + 2 = 19, 1 + 9 = 10, 1 + 0 = 1; a(12) = 1.

%p A190998:=proc(n) local d, i, s: d:=numtheory[divisors](n): s:=0: for i from 1 to nops(d) do s:=s+((d[i]-1) mod 9)+1: if(s>=10)then s:=((s-1) mod 9)+1: fi: od: return s: end: seq(A190998(n), n=1..105); # _Nathaniel Johnston_, Jun 15 2011

%Y Cf. A134681, A034690, A190997.

%K nonn,easy,base

%O 1,2

%A _Jaroslav Krizek_, Jun 15 2011