A263470 Total number of positive integers < 10^n with multiplicative digital root value 0.

0, 24, 476, 6739, 82401, 902608, 9394517, 96122290, 975700392, 9854082822, 99180099587, 995679223590, 9977627937023, 99879659224379, 999321444658475, 9996118748668338, 99978099721506172, 999879067589400315, 9999346524827012003, 99996542810942397874

Offset: 1

Author

Martin Renner, Oct 19 2015

Keywords

• nonn
• base

Comments

Partial sums of A263476. - Michel Marcus, Oct 22 2015

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..50
• Eric Weisstein's World of Mathematics, Multiplicative Digital Root.

Crossrefs

Cf. A031347, A034048, A263476.

Programs

Mathematica

Length@ Select[Range[10^# - 1], FixedPoint[Times @@ IntegerDigits@ # &, #] == 0 &] & /@ Range@ 6 (* Michael De Vlieger, Oct 19 2015 *)

PARI

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

Formula

a(n) + A000027(n) + A263471(n) + A000217(n) + A263472(n) + A263473(n) + A263474(n) + A000217(n) + A263475(n) + A000292(n) = A002283(n).

Extensions

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