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

1,2

Comments

First differences of A263470.

Links

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A031347, A034048, A263470.

Sequence in context: A024303 A060195 A114201 * A263470 A276816 A200979

Adjacent sequences: A263473 A263474 A263475 * A263477 A263478 A263479

Keyword

nonn,base

Author

Martin Renner, Oct 19 2015

Extensions

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

Status

approved