* 42 is a pronic spot and an abundant heel; its ancient factorisation 2 · 3 · 7 makes it the second sphenic get along and as well as 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 besides the second sphenic number to be bracketed by twin primes; 30 is also a pronic number and also rests between two primes. 42 has a 14 genus Phallus aliquot successiveness 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 Sylvesters sequence; deal the first five such numbers it is also a primary pseudoperfect number.
* It is a Catalan number. Consequently; 42 is the number of noncrossing partitions of a set of five elements, the number of triangulations of a heptagon, the number of rooted orderinged binary trees with six leaves, the number of ways in which five pairs of nested parentheses can be arranged, etc.
* It is the reciprocal of the ordinal 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 & angstrom; Ghosh have conjectured
where the infinite product is over all prime numbers, p.[1][2]
* It is the third pentadecagonal number. It is a meandric number and an open meandric number.
* 42 is a Størmer number.
* 42 is a perfect score on the ground forces Math Olympiad (USAMO)[3] and International Mathematical Olympiad (IMO).[4]
* In base 10, this number is a Harshad number and a self number, while it is a repdigit in base 4 (as 222).
[edit] Science
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