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User:Peter Luschny/MyFabInt

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My favorite integer

In the meantime I decided to make 32760 my favorite integer. Here are some reasons why 32760 is an interesting number as it is also a member of the following sequences.

A000793Landau's function g(n): largest order of permutation of n elements.
Equivalently, largest lcm of partitions of n.
A001599Harmonic or Ore numbers: numbers n such that harmonic mean
of divisors of n is an integer.
A001763Number of dissections of a ball: (3n+3)!/(2n+3)!.
A002790Denominators of Cauchy numbers of second type.
A006953Denominator of Bernoulli(2n)/2n.
A007340Numbers n such that both the harmonic and arithmetic means of
the divisors of n are integers.
A007691Multiply-perfect numbers: n divides sigma(n).
A027598Numbers n such that the set of prime divisors of n is equal to
the set of prime divisors of sigma(n).
A0276874-perfect (quadruply-perfect or sous-triple) numbers:
sum of divisors of n is 4n.
A034722Products of successive Fibonacci numbers.
A035527Harmonic seed numbers.
A045625Number of n-bead black-white reversible strings with
fundamental period n.
A046985Multiply perfect numbers whose average divisor is an integer
and divides the number itself.
A051549LCM { sigma(1), ..., sigma(n) }.
A051593Largest order of even permutation of n elements, or maximal order
of element of alternating group A_n.
A051703Maximal value of products of partitions of n into powers of
distinct primes.
A052762Products of 4 consecutive integers.
A063067Numbers expressible as (a^2-1)(b^2-1) in at least 2
distinct ways [b>=a>1].
A065932Index values for new maxima in sequence A007365.
A066289Numbers n such that Mod[DivisorSigma[2k-1,n],n]=0 holds for all k;
i.e. all odd-power-sums of divisors of n are divisible by n.
A067151Number of regions in regular n-gon which are 4-gons.
A067234Numbers n such that phi(4n+1)=sigma(n).
A068969Areas of integer Heronian triangles.
A069070Numbers n such that n*sigma(n) is a perfect square.
A071707Numbers n such that n divides tau(n)*sigma(n).
A074167Product of prime divisors of composite numbers between
consecutive primes.
A084174Generalized Jacobsthal numbers.
A090777Numbers n such that sigma(n) divides n^2.
A092003Numbers that can be expressed as the difference of the squares of
primes in exactly seven distinct ways.
A093687Total number of 1's in binary expansion of all divisors of n sets
 a new record.
A099830Smallest perimeter S such that exactly n distinct Pythagorean
triangles with this perimeter can be constructed.
A114887Multiperfect numbers sigma(n)=k*n, which are divisible by the
sum of their prime factors without repetition.
A120834Denominators of partial sums of (p+q)/p*q, where p and q are primes.
A121287Numbers such that Sigma(n)*UnitarySigma(n) is divisible
by UnitaryPhi(n)*n.
A129650Largest order of a permutation of n elements with exactly 5 cycles.
Also the largest LCM of a 5-partition of n.
A181312Highly abundant numbers n whose largest prime factor is
greater than log(n).
A181504A000272(n+1) - A000951(n), n >= 6. Number of forests of rooted
labeled trees with n nodes and height >= 5.