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a(n) = the smallest positive integer with exactly n divisors and that, when represented in binary, contains the binary representation of n as a substring.
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%I #22 Jun 25 2017 02:47:29

%S 1,2,25,8,81,12,15625,24,36,80,9765625,60,531441,448,1936,264,

%T 152587890625,288,3814697265625,336,10816,11264,2384185791015625,480,

%U 234256,53248,1764,960,459986536544739960976801,1008,931322574615478515625,1920,295936,1114112

%N a(n) = the smallest positive integer with exactly n divisors and that, when represented in binary, contains the binary representation of n as a substring.

%C If n is prime, then a(n) = p^(n-1) for some prime p (if a(n) exists) as all numbers with n divisors are of this form. - _Chai Wah Wu_, Dec 04 2014

%H Chai Wah Wu, <a href="/A161575/b161575.txt">Table of n, a(n) for n = 1..34</a>

%e The positive integers with exactly 5 divisors are 16 (10000 in binary), 81 (1010001 in binary), etc. 81 is the smallest of these which contains the binary representation of 5 (101) as a substring. (Like this: {101}0001.) So a(5) = 81.

%K base,nonn

%O 1,2

%A _Leroy Quet_, Jun 14 2009

%E More terms from _Sean A. Irvine_, Feb 17 2010

%E More terms from _Chai Wah Wu_, Dec 04 2014