42 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 Rieman zeta function".

In particular, Conrey & Ghosh have conjectured:

where the infinite product is over all prime numbers.

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 ): 4 2 = 2 4 = 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.)

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).

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.

And it rocks the freaking house. Word.