A263476 - OEIS

%I #26 Oct 25 2015 06:58:54

%S 0,24,452,6263,75662,820207,8491909,86727773,879578102,8878382430,

%T 89326016765,896499124003,8981948713433,89902031287356,

%U 899441785434096,8996797304009863,89981980972837834,899900967867894143,8999467457237611688,89997196286115385871

%N Total number of n-digit positive integers with multiplicative digital root value 0.

%C First differences of A263470.

%H Hiroaki Yamanouchi, <a href="/A263476/b263476.txt">Table of n, a(n) for n = 1..50</a>

%F a(n) + A000012(n) + A263477(n) + A000027(n) + A263478(n) + A263479(n) + A263480(n) + A000027(n) + A263481(n) + A000217(n) = A052268(n).

%t Last /@ Tally@ IntegerLength@ Select[Range[0, 10^6 - 1], FixedPoint[Times @@ IntegerDigits@ # &, #] == 0 &] (* _Michael De Vlieger_, Oct 21 2015 *)

%o (PARI) t(k) = {while(k>9, k=prod(i=1, #k=digits(k), k[i])); k}

%o a(n) = sum(i=10^(n-1), 10^n - 1, if(t(i) == 0, 1, 0));  \\ _Altug Alkan_, Oct 19 2015

%Y Cf. A031347, A034048, A263470.

%K nonn,base

%O 1,2

%A _Martin Renner_, Oct 19 2015

%E a(9)-a(20) from _Hiroaki Yamanouchi_, Oct 25 2015