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121 number - In mathematics

121 number - In mathematics: Encyclopedia II - 121 number - In mathematics

One hundred twenty-one is a square and is the sum of three consecutive primes (37 + 41 + 43). There are no squares besides 121 known to be of the form 1 + p + p2 + p3 + p4, where p is prime (3, in this case). There are only two other squares known to be of the form n! + 1. It is also a star number and a centered octagonal number. In base 10, it is a Smith number since its digits add up to the same value as its factorization ( ...

121 number: Encyclopedia II - 121 number - In mathematics

121 number - In mathematics

One hundred twenty-one is a square and is the sum of three consecutive primes (37 + 41 + 43). There are no squares besides 121 known to be of the form 1 + p + p² + p³ + p⁴, where p is prime (3, in this case). There are only two other squares known to be of the form n! + 1.

It is also a star number and a centered octagonal number.

In base 10, it is a Smith number since its digits add up to the same value as its factorization (which uses the same digits) and as a consequence of that it is a Friedman number. But it can not be expressed as the sum of any other number plus that number's digits, making 121 a self number.