A263476 Total number of n-digit positive integers with multiplicative digital root value 0.

0, 24, 452, 6263, 75662, 820207, 8491909, 86727773, 879578102, 8878382430, 89326016765, 896499124003, 8981948713433, 89902031287356, 899441785434096, 8996797304009863, 89981980972837834, 899900967867894143, 8999467457237611688, 89997196286115385871

Offset: 1

Author

Martin Renner, Oct 19 2015

Keywords

• nonn
• base

Comments

First differences of A263470.

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A031347, A034048, A263470.

Programs

Mathematica

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

PARI

t(k) = {while(k>9, k=prod(i=1, #k=digits(k), k[i])); k}
a(n) = sum(i=10^(n-1), 10^n - 1, if(t(i) == 0, 1, 0));  \\ Altug Alkan, Oct 19 2015

Formula

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

Extensions

a(9)-a(20) from Hiroaki Yamanouchi, Oct 25 2015