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%I #20 Sep 08 2022 08:45:43
%S 1,1,1,2,1,3,1,4,3,5,1,6,1,7,5,8,1,9,1,10,7,11,1,12,5,13,9,2,1,15,1,
%T 16,11,17,35,18,1,19,13,20,1,21,1,22,3,23,1,24,7,25,17,26,1,27,55,28,
%U 19,29,1,30,1,31,21,32,13,33,1,34,23,5,1,36,1,37,25,38,77,39,1,40,27,41,1,42
%N a(n) = the smallest positive integer such that a(n) *(2^n -2) is a multiple of n.
%C This is not the same sequence as sequence A032742, where A032742(n) = the largest proper divisor of n. See A146077 for numbers n such that the sequences A032742 and A159353 differ.
%H Michael De Vlieger, <a href="/A159353/b159353.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = Denominator((2^n - 2)/n). - _Juri-Stepan Gerasimov_, Sep 09 2014
%t Array[Block[{k = 1}, While[! Divisible[k (2^# - 2), #], k++]; k] &, 84] (* _Michael De Vlieger_, Oct 30 2017 *)
%o (Magma) [Denominator((2^n-2)/n): n in [1..84]]; // _Juri-Stepan Gerasimov_, Sep 09 2014
%o (PARI) a(n)=my(k=1);while((2^n-2)*k%n != 0,k++);return(k) \\ _Edward Jiang_, Sep 09 2014
%o (PARI) a(n)=denominator(lift(Mod(2,n)^n-2)/n) \\ _Charles R Greathouse IV_, Sep 11 2014
%Y Cf. A000918, A146077.
%K nonn
%O 1,4
%A _Leroy Quet_, Apr 11 2009
%E Extended by _Ray Chandler_, Apr 11 2009
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