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A078267 Smallest k such that k*N is an integer where N is obtained by placing the string "n" after a decimal point.

%I A078267 #26 Oct 08 2021 03:12:33
%S A078267 10,5,10,5,2,5,10,5,10,10,100,25,100,50,20,25,100,50,100,5,100,50,100,
%T A078267 25,4,50,100,25,100,10,100,25,100,50,20,25,100,50,100,5,100,50,100,25,
%U A078267 20,50,100,25,100,2,100,25,100,50,20,25,100,50,100,5,100,50,100,25,20
%N A078267 Smallest k such that k*N is an integer where N is obtained by placing the string "n" after a decimal point.
%C A078267 From _Jaroslav Krizek_, Feb 05 2010: (Start)
%C A078267 a(n) is the denominator of fraction a/b, where gcd(a, b) = 1, such that its decimal representation has form 0.(n).
%C A078267 The numerators are in A078268. Example: a(6) = 5; 3/5 = 0.6.
%C A078267 (End)
%H A078267 Michael De Vlieger, <a href="/A078267/b078267.txt">Table of n, a(n) for n = 1..10000</a>
%F A078267 a(10^m) = 10, a(r*10^m) = a(r).
%F A078267 a(n) = (A078268(n)*10^A055642(n)) / n. [_Jaroslav Krizek_, Feb 05 2010]
%F A078267 a(n) = 10^A055642(n)/gcd(n, 10^A055642(n)). - _Michael S. Branicky_, Oct 05 2021
%e A078267 a(40) = 5 since 5*0.40 = 2 is an integer. a(1) = a(10) = 10.
%t A078267 Array[#2/GCD[#1, #2] & @@ {#, 10^IntegerLength[#]} &, 65] (* _Michael De Vlieger_, Oct 05 2021 *)
%o A078267 (PARI) a(n) = denominator(n/10^(#Str(n))); \\ _Michel Marcus_, Mar 31 2019
%o A078267 (Python)
%o A078267 from math import gcd
%o A078267 def a(n): b = 10**len(str(n)); return b//gcd(n, b)
%o A078267 print([a(n) for n in range(1, 103)]) # _Michael S. Branicky_, Oct 05 2021
%Y A078267 Cf. A055642, A078268.
%K A078267 base,frac,nonn
%O A078267 1,1
%A A078267 _Amarnath Murthy_, Nov 24 2002
%E A078267 Edited and extended by _Henry Bottomley_, Dec 08 2002