Number Gossip

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Unique Properties of 9075

9075 is the smallest odd number n such that 2φ(n) < n, but there does not exist even k < n with φ(k) = φ(n)

Common Properties of 9075

Apocalyptic power

The number n is called an apocalyptic power if 2ⁿ contains the consecutive digits 666 (in decimal).

...,
9071,
9073,
9074,
9075,
9076,
9077,
9078,
...

Composite

A positive integer greater than 1 that is not prime is called composite.

Composite numbers are opposite to prime numbers.

...,
9072,
9073,
9074,
9075,
9076,
9077,
9078,
...

Deficient

The number n is deficient if the sum of all its positive divisors except itself is less than n.

Compare with perfect and abundant numbers.

...,
9071,
9073,
9074,
9075,
9076,
9077,
9079,
...

Evil

The number n is evil if it has an even number of 1's in its binary expansion.

Guess what odious numbers are.

...,
9069,
9070,
9072,
9075,
9077,
9078,
9081,
...

Lucky

To build the lucky number sequence, start with natural numbers. Delete every second number, leaving 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, ... . The second number remaining is 3, so delete every third number, leaving 1, 3, 7, 9, 13, 15, 19, 21, ... . The next number remaining is 7, so delete every 7th number, leaving 1, 3, 7, 9, 13, 15, 21, ... . The next number remaining is 9, so delete every ninth number, etc.

Those numbers were lucky they weren't crossed out.

...,
9061,
9063,
9073,
9075,
9081,
9085,
9115,
...

Odd

A number is odd if it is not divisible by 2.

Numbers that are not odd are even. Compare with another pair -- evil and odious numbers.

...,
9069,
9071,
9073,
9075,
9077,
9079,
9081,
...

Tanya Khovanova

Number Gossip

Unique Properties of 9075

Common Properties of 9075