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

Author

Amarnath Murthy, Aug 18 2002

Keywords

• nonn
• base

Comments

Here 0 is regarded as not divisible by any number.

a(n) = 0 if 5 divides n or n contains a prime divisor > 9. - Sascha Kurz, Aug 23 2002 [Corrected by Sean A. Irvine, Dec 23 2024]

Crossrefs

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

Programs

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);

Formula

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

Extensions

More terms from Sascha Kurz, Aug 23 2002