Number Gossip
(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)
Unique Properties of 77
- 77 is the smallest number with multiplicative persistence 4
- 77 is the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1
- 77 is the smallest number n such that the smallest possible number of multiplications required to compute x to the n-th power is by 1 fewer than the number of multiplications obtained by Knuth's power tree method
- 77 In English, seventy-seven has the largest number of syllables among numbers below 100
Common Properties of 77
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime numbers.
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.
The number n is evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
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.
A palindrome is a number that reads the same forward or backward.
A number is said to be square-free if its prime decomposition contains no repeated factors.
The next Ulam number is uniquely the sum of two earlier distinct Ulam numbers.