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

1,2

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.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A031347, A034048, A263476.

Sequence in context: A376283 A114201 A263476 * A276816 A200979 A361576

Adjacent sequences: A263467 A263468 A263469 * A263471 A263472 A263473

Keyword

nonn,base

Author

Martin Renner, Oct 19 2015

Extensions

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

Status

approved