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150 (number)
| Field | Value |
|---|---|
| number | 150 |
| divisor | 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150 |
150 (one hundred [and] fifty) is the natural number following 149 and preceding 151.
In mathematics
- 150 is the sum of eight consecutive primes (7 + 11 + 13 + 17 + 19 + 23 + 29 + 31). Given 150, the Mertens function returns 0.
- 150 is conjectured to be the only minimal difference greater than 1 of any increasing arithmetic progression of n primes (in this case, n = 7) that is not a primorial (a product of the first m primes).
- The sum of Euler's totient function φ(x) over the first twenty-two integers is 150.
- 150 is a Harshad number and an abundant number.
- 150 degrees is the measure of the internal angle of a regular dodecagon.
In other fields
150 is also:
- The number of degrees in the quincunx astrological aspect explored by Johannes Kepler.
- The approximate value for Dunbar's number, a theoretical value with implications in sociology and anthropology. It is actually 148.
References
References
- "Sloane's A028442 : Numbers n such that Mertens' function is zero". OEIS Foundation.
- "Sloane's A123556: Minimal difference of any increasing arithmetic progression of n primes.". OEIS Foundation.
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