A231817 Multiplicative digital root of concatenation of all divisors of n (A037278).

1, 2, 3, 8, 5, 8, 7, 8, 4, 0, 1, 6, 3, 0, 5, 0, 7, 0, 9, 0, 8, 8, 6, 8, 0, 4, 6, 0, 8, 0, 3, 0, 4, 6, 0, 0, 2, 8, 8, 0, 4, 0, 2, 0, 0, 6, 6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 6, 4, 0, 0, 0, 0, 8, 0, 2, 0, 7, 0, 2, 8, 0, 0, 8, 0, 8, 0, 0, 6, 8, 0, 0, 0, 0

Offset: 1

Author

Jaroslav Krizek, Nov 13 2013

Keywords

• nonn
• base

Comments

Also multiplicative digital root of A190997 (product of digits of all the divisors of n) or A007955 (product of divisors of n).

Conjecture: a(n) = 0 for almost all n.

793 of the first 1000 terms are zeros, and 9147 out of the first 10000 terms are zeros. - Harvey P. Dale, Jul 30 2019

Examples

			For n=12: 1*2*3*4*6*1*2=288, 2*8*8=128, 1*2*8=16, 1*6=6; a(12)=6.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A037278, A007955, A190998 (associative digital root of digits of all the divisors of n), A031347 (multiplicative digital root of n).

Programs

Mathematica

Table[NestWhile[Times@@IntegerDigits[#]&,Times@@Flatten[ IntegerDigits/@ Divisors[ n]], #>9&],{n,90}] (* Harvey P. Dale, Jul 30 2019 *)