A190998 Digital root of concatenation of all divisors of n (A037278).

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, 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, 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

Offset: 1

Author

Jaroslav Krizek, Jun 15 2011

Keywords

• nonn
• easy
• base

Comments

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

Also digital root of A000203 (sum of divisors of n). - Michel Marcus, Sep 13 2014

Examples

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

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A134681, A034690, A190997.

Programs

Maple

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