It is a
composite number; its
factorization makes it the second
sphenic number and also the second of the form {2.3.r}. As with all
sphenic numbers of this form the
aliquot sum is
abundant by 12. 42 is also the second sphenic number to be bracketed by
twin primes;
30 also rests between two primes. 42 has a 14 member aliquot sequence 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0 and is itself part of the
aliquot sequence commencing with the first sphenic number
30. Further, 42 is the 10th member of the 3-aliquot tree.
42 is the product of the first three terms of
Sylvester's sequence; like the first four such numbers it is also a
primary pseudoperfect number.
It is the sum of the
totient function for the first eleven integers.
It is a
Catalan number.
It is the reciprocal of a
Bernoulli number.
It is conjectured to be the scaling factor in the leading order term of the "sixth
moment of the
Riemann zeta function". In particular, Conrey & Ghosh have conjectured
where the
infinite product is over all prime numbers,
p.
[1] [2]
It is a
pronic number, and the third 15
-gonal number. It is a
meandric number and an
open meandric number.
42 is a perfect score on the USA Math Olympiad (
USAMO) and
International Mathematical Olympiad (IMO).
In base 10, this number is a
Harshad number and a
self number, while it is a
repdigit in base 4 (as 222).
The eight digits of
pi beginning from 242,422 places after the decimal point are 42424242.
The first digit (
4) taken to the power of the second digit (
2) is equal to the second digit (
2) taken to the power of the first digit (
4): 42 = 24 = 16. It follows clearly that
24 exhibits the same characteristic, and in fact 24 is the only other two-digit non-
repdigit number that does. (All two-digit repdigit numbers exhibit this characteristic.)
Given 27 same-size cubes whose nominal values progress from 1 to 27, a 3x3x3 "magic cube" can be constructed such that every row, column and corridor, and every diagonal passing through the center, comprises 3 cubes whose sum of values is 42.