420 (number)

For other uses, see 420 (disambiguation).

← 419 420 421 →
List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	four hundred twenty
Ordinal	420th (four hundred twentieth)
Factorization	2^2 × 3 × 5 × 7
Greek numeral	ΥΚ´
Roman numeral	CDXX
Binary	1101001002
Ternary	1201203
Senary	15406
Octal	6448
Duodecimal	2B012
Hexadecimal	1A416

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

In mathematics

420 is:

• the sum of four consecutive primes (${\displaystyle 101+103+107+109}$).
• the sum of the first twenty 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 from 1 to 7; as a consequence of that, it is a Harshad number in bases 2 to 10, except in base 5.
• a 141-gonal number.
• a balanced number.^[4]

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 the day being notated as 4/20 in the month-day-year format. Because of these associations, 420 has been humorously referred to as the "weed number". "Weed" is a slang term for cannabis.
• 420 is the country calling code for Czech Republic.

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.
4. Sloane, N. J. A. (ed.). "Sequence A020492 (Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.