login
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.
4
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
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
KEYWORD
nonn,base
AUTHOR
Amarnath Murthy, Aug 18 2002
EXTENSIONS
More terms from Sascha Kurz, Aug 23 2002
STATUS
approved