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, 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

Chai Wah Wu, Table of n, a(n) for n = 1..34

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

Adjacent sequences: A161572 A161573 A161574 * A161576 A161577 A161578

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