A263474 Total number of positive integers < 10^n with multiplicative digital root value 6.

1, 14, 155, 1172, 6843, 43538, 318457, 2223803, 14185700, 84670477, 477808607, 2577052118, 13759255632, 75251167843, 418157757456, 2267313716636, 11616142299625, 55909713312571, 257522103127082, 1182251998919171, 5791219719115580, 32715779086392723

Offset: 1

Author

Martin Renner, Oct 19 2015

Keywords

• nonn
• base

Comments

Partial sums of A263480.

Links

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

Crossrefs

Cf. A031347, A034053, A263480.

Programs

Mathematica

lim = 6; t = Select[Range[1, 10^lim - 1], FixedPoint[Times @@ IntegerDigits@ # &, #] == 6 &]; Count[t, n_ /; n <= 10^#] & /@ Range@ lim (* 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=1, 10^n - 1, if(t(i) == 6, 1, 0)); \\ Altug Alkan, Oct 19 2015

Formula

A263470(n) + A000027(n) + A263471(n) + A000217(n) + A263472(n) + A263473(n) + a(n) + A000217(n) + A263475(n) + A000292(n) = A002283(n).

Extensions

a(9)-a(22) from Hiroaki Yamanouchi, Oct 25 2015