42 In mathematics
Forty-two 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
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