A034048 - OEIS

%I #29 Jul 21 2020 17:13:14

%S 0,10,20,25,30,40,45,50,52,54,55,56,58,59,60,65,69,70,78,80,85,87,90,

%T 95,96,100,101,102,103,104,105,106,107,108,109,110,120,125,130,140,

%U 145,150,152,154,155,156,158,159,160,165,169,170,178,180,185,187,190,195

%N Numbers with multiplicative digital root value 0.

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

%C This sequence has density 1. - _Franklin T. Adams-Watters_, Apr 01 2009

%C Any integer with at least one 0 among its base 10 digits is in this sequence. - _Alonso del Arte_, Aug 29 2014

%C 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

%H Franklin T. Adams-Watters, <a href="/A034048/b034048.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiplicativeDigitalRoot.html">Multiplicative Digital Root</a>

%H <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.

%e 20 is in the sequence because 2 * 0 = 0.

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

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

%o (PARI) is(n)=factorback(digits(n))==0 \\ _Charles R Greathouse IV_, Feb 13 2017

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

%Y Cf. the subsets A011540 and A008592.

%K nonn,base,easy

%O 1,2

%A _Patrick De Geest_, Sep 15 1998