A super-Poulet number is a
Poulet number Poulet is a French surname, meaning chicken. Notable people with the name include:
* Anne Poulet (born 1942), American art historian
* Gaston Poulet (1892–1974), French violinist and conductor
* Georges Poulet (1902–1991), Belgian literary cri ...
, or pseudoprime to base 2, whose every
divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by ...
''d'' divides
:2
''d'' − 2.
For example, 341 is a super-Poulet number: it has positive divisors and we have:
:(2
11 - 2) / 11 = 2046 / 11 = 186
:(2
31 - 2) / 31 = 2147483646 / 31 = 69273666
:(2
341 - 2) / 341 = 13136332798696798888899954724741608669335164206654835981818117894215788100763407304286671514789484550
When
is not prime, then it and every divisor of it are a pseudoprime to base 2, and a super-Poulet number.
The super-Poulet numbers below 10,000 are :
Super-Poulet numbers with 3 or more distinct prime divisors
It is relatively easy to get super-Poulet numbers with 3 distinct prime divisors. If you find three Poulet numbers with three common prime factors, you get a super-Poulet number, as you built the product of the three prime factors.
Example:
2701 = 37 * 73 is a Poulet number,
4033 = 37 * 109 is a Poulet number,
7957 = 73 * 109 is a Poulet number;
so 294409 = 37 * 73 * 109 is a Poulet number too.
Super-Poulet numbers with up to 7 distinct
prime factor
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
s you can get with the following numbers:
*
*
*
*
For example, 1118863200025063181061994266818401 = 6421 * 12841 * 51361 * 57781 * 115561 * 192601 * 205441 is a super-Poulet number with 7 distinct prime factors and 120 Poulet numbers.
External links
*
Numericana{{Classes of natural numbers
Integer sequences