A034048 Numbers with multiplicative digital root value 0.

0, 10, 20, 25, 30, 40, 45, 50, 52, 54, 55, 56, 58, 59, 60, 65, 69, 70, 78, 80, 85, 87, 90, 95, 96, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 120, 125, 130, 140, 145, 150, 152, 154, 155, 156, 158, 159, 160, 165, 169, 170, 178, 180, 185, 187, 190, 195

Offset: 1

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base
• easy

Comments

Numbers with root value 1 are the 'repunits' (see A000042).

This sequence has density 1. - Franklin T. Adams-Watters, Apr 01 2009

Any integer with at least one 0 among its base 10 digits is in this sequence. - Alonso del Arte, Aug 29 2014

This sequence is 10-automatic: it contains numbers with a 0, or with a 5 and any even digit. - Charles R Greathouse IV, Feb 13 2017

Examples

			20 is in the sequence because 2 * 0 = 0.
25 is in the sequence because 2 * 5 = 10 and 1 * 0 = 0.
		

Links

• Franklin T. Adams-Watters, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Multiplicative Digital Root
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A031347, A034048, A002275, A034049, A034050, A034051, A034052, A034053, A034054, A034055, A034056 (numbers having multiplicative digital roots 0-9).

Cf. the subsets A011540 and A008592.

Programs

Mathematica

mdr0Q[n_]:=NestWhile[Times@@IntegerDigits[#]&,n,#>9&]==0; Select[Range[ 0,200],mdr0Q] (* Harvey P. Dale, Jul 21 2020 *)

PARI

is(n)=factorback(digits(n))==0 \\ Charles R Greathouse IV, Feb 13 2017