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URL: https://oeis.org/A161575

⇱ A161575 - OEIS

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A161575
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.
1
1, 2, 25, 8, 81, 12, 15625, 24, 36, 80, 9765625, 60, 531441, 448, 1936, 264, 152587890625, 288, 3814697265625, 336, 10816, 11264, 2384185791015625, 480, 234256, 53248, 1764, 960, 459986536544739960976801, 1008, 931322574615478515625, 1920, 295936, 1114112
OFFSET
1,2
COMMENTS
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
LINKS
EXAMPLE
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.
CROSSREFS
Sequence in context: A065665 A321350 A249634 * A036502 A076449 A153811
KEYWORD
base,nonn
AUTHOR
Leroy Quet, Jun 14 2009
EXTENSIONS
More terms from Sean A. Irvine, Feb 17 2010
More terms from Chai Wah Wu, Dec 04 2014
STATUS
approved