Number Gossip

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Unique Properties of 535

535 is the smallest multidigit palindrome n such that φ(n) is also a palindrome (φ(535) = 424)

Common Properties of 535

Composite

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

Composite numbers are opposite to prime numbers.

...,
532,
533,
534,
535,
536,
537,
538,
...

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.

...,
530,
531,
533,
535,
536,
537,
538,
...

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.

...,
517,
519,
529,
535,
537,
541,
553,
...

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.

...,
529,
531,
533,
535,
537,
539,
541,
...

Odious

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

Guess what evil numbers are.

...,
529,
530,
532,
535,
536,
539,
541,
...

Palindrome

A palindrome is a number that reads the same forward or backward.

...,
505,
515,
525,
535,
545,
555,
565,
...

Smith (Joke)

A composite number is called a Smith number if the sum of its digits equals the sum of all the digits appearing in its prime divisors (counting multiplicity).

In 1984, when Albert Wilansky called his brother-in-law, named Smith, he noticed that the phone number possesses the property described here. Are they called joke numbers, because they were named after an innocent unsuspecting brother-in-law :-) ?

...,
483,
517,
526,
535,
562,
576,
588,
...

Square-free

A number is said to be square-free if its prime decomposition contains no repeated factors.

...,
530,
533,
534,
535,
537,
538,
541,
...

Undulating

Undulating numbers are numbers of the form abababab... in base 10.

This property is significant starting from 3-digit numbers, so we will not consider numbers below 100.

...,
505,
515,
525,
535,
545,
555,
565,
...

Tanya Khovanova

Number Gossip

Unique Properties of 535

Common Properties of 535