420 (number)

From Wikipedia, the free encyclopedia
For other uses, see 420 (disambiguation).
← 419 420 421 →
List of numbers — Integers
← 0 100 200 300 400 500 600 700 800 900 →
Cardinalfour hundred twenty
Ordinal420th
(four hundred twentieth)
Factorization22 × 3 × 5 × 7
Greek numeralΥΚ´
Roman numeralCDXX
Binary1101001002
Ternary1201203
Octal6448
Duodecimal2B012
Hexadecimal1A416

420 (four hundred [and] twenty) is the natural number following 419 and preceding 421.

In mathematics[]

420 is:

  • the sum of four consecutive primes (101 + 103 + 107 + 109).
  • the sum of the first 20 positive even numbers.
  • a zero of the Mertens function[1] and is sparsely totient.[2]
  • a pronic number.[3]
  • the smallest number divisible by the numbers 1 to 7, and as a consequence of that it is a Harshad number in every base from 2 to 10 except base 5.
  • a 141-gonal number.
  • a Harshad number.

In other fields[]

  • 420 is a slang term that refers to the consumption of cannabis. April 20th is commonly celebrated as a holiday dedicated to the drug, due to the numerical form of the day being 4/20.
  • 420 is the country calling code for Czech Republic.
  • 4/20 as a date (April 20th) is also widely known as the birthday of German dictator Adolf Hitler.

References[]

  1. ^ "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
  2. ^ "Sloane's A036913 : Sparsely totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
  3. ^ "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
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