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 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. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 11 12:31 EDT 2024. Contains 375829 sequences. (Running on oeis4.)