A073912 Smallest number m such that m and the product of digits of m are both divisible by 8n, or 0 if no such number exists.

8, 48, 168, 288, 0, 384, 728, 448, 1368, 0, 0, 384, 0, 784, 0, 2688, 0, 3168, 0, 0, 7896, 0, 0, 2688, 0, 0, 4968, 12768, 0, 0, 0, 4864, 0, 0, 0, 4896, 0, 0, 0, 0, 0, 8736, 0, 0, 0, 0, 0, 2688, 74872, 0, 0, 0, 0, 22896, 0, 14784, 0, 0, 0, 0, 0, 0, 33768, 14848, 0, 0, 0, 0, 0

Offset

1,1

Comments

Here 0 is regarded as not divisible by any number.

a(n) = 0 if 10 divides n or n contains a prime divisor > 9. - Sascha Kurz, Aug 23 2002

Links

Table of n, a(n) for n=1..69.

Formula

a(n) = A085124(8*n). - R. J. Mathar, Jun 21 2018

Maple

f := 8:for i from 1 to 400 do b := ifactors(f*i)[2]: if b[nops(b)][1]>9 or (f*i mod 10) =0 then a[i] := 0:else j := 0:while true do j := j+f*i:c := convert(j, base, 10): d := product(c[k], k=1..nops(c)): if (d mod f*i)=0 and d>0 then a[i] := j:break:fi: od:fi:od:seq(a[k], k=1..400);

Crossrefs

Cf. A073906, A085124, A073908, A073909, A073910, A073911.

Sequence in context: A209443 A072819 A190317 * A212571 A247727 A187174

Adjacent sequences: A073909 A073910 A073911 * A073913 A073914 A073915

Keyword

nonn,base

Author

Amarnath Murthy, Aug 18 2002

Extensions

More terms from Sascha Kurz, Aug 23 2002

Status

approved