A073908 Smallest number m such that m and the product of digits of m are both divisible by 7n, or 0 if no such number exists.

7, 378, 273, 476, 175, 378, 3577, 728, 1197, 0, 0, 672, 0, 7742, 735, 784, 0, 3276, 0, 0, 7497, 0, 0, 7896, 1575, 0, 7938, 69776, 0, 0, 0, 12768, 0, 0, 37975, 3276, 0, 0, 0, 0, 0, 71736, 0, 0, 9765, 0, 0, 8736, 47677, 0, 0, 0, 0, 7938, 0, 74872, 0, 0, 0, 0, 0, 0, 7497

Offset

1,1

Comments

Here 0 is regarded as not divisible by any number.

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

Links

Table of n, a(n) for n=1..63.

Formula

a(n) = A085124(7*n). - R. J. Mathar, Jun 21 2018

Example

a(8) = 728 is divisible by 7*8 = 56 and also 7*2*8 = 112 = 2*56.

Maple

f := 7: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, A073909, A073910, A073911, A073912.

Sequence in context: A261824 A084001 A238632 * A250345 A201114 A027510

Adjacent sequences: A073905 A073906 A073907 * A073909 A073910 A073911

Keyword

nonn,base

Author

Amarnath Murthy, Aug 18 2002

Extensions

More terms from Sascha Kurz, Aug 23 2002

Status

approved