User:Peter Luschny/MyFabInt

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.

A000793	Landau's function g(n): largest order of permutation of n elements. Equivalently, largest lcm of partitions of n.
A001599	Harmonic or Ore numbers: numbers n such that harmonic mean of divisors of n is an integer.
A001763	Number of dissections of a ball: (3n+3)!/(2n+3)!.
A002790	Denominators of Cauchy numbers of second type.
A006953	Denominator of Bernoulli(2n)/2n.
A007340	Numbers n such that both the harmonic and arithmetic means of the divisors of n are integers.
A007691	Multiply-perfect numbers: n divides sigma(n).
A027598	Numbers n such that the set of prime divisors of n is equal to the set of prime divisors of sigma(n).
A027687	4-perfect (quadruply-perfect or sous-triple) numbers: sum of divisors of n is 4n.
A034722	Products of successive Fibonacci numbers.
A035527	Harmonic seed numbers.
A045625	Number of n-bead black-white reversible strings with fundamental period n.
A046985	Multiply perfect numbers whose average divisor is an integer and divides the number itself.
A051549	LCM { sigma(1), ..., sigma(n) }.
A051593	Largest order of even permutation of n elements, or maximal order of element of alternating group A_n.
A051703	Maximal value of products of partitions of n into powers of distinct primes.
A052762	Products of 4 consecutive integers.
A063067	Numbers expressible as (a^2-1)(b^2-1) in at least 2 distinct ways [b>=a>1].
A065932	Index values for new maxima in sequence A007365.
A066289	Numbers 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.
A067151	Number of regions in regular n-gon which are 4-gons.
A067234	Numbers n such that phi(4n+1)=sigma(n).
A068969	Areas of integer Heronian triangles.
A069070	Numbers n such that n*sigma(n) is a perfect square.
A071707	Numbers n such that n divides tau(n)*sigma(n).
A074167	Product of prime divisors of composite numbers between consecutive primes.
A084174	Generalized Jacobsthal numbers.
A090777	Numbers n such that sigma(n) divides n^2.
A092003	Numbers that can be expressed as the difference of the squares of primes in exactly seven distinct ways.
A093687	Total number of 1's in binary expansion of all divisors of n sets  a new record.
A099830	Smallest perimeter S such that exactly n distinct Pythagorean triangles with this perimeter can be constructed.
A114887	Multiperfect numbers sigma(n)=k*n, which are divisible by the sum of their prime factors without repetition.
A120834	Denominators of partial sums of (p+q)/p*q, where p and q are primes.
A121287	Numbers such that Sigma(n)*UnitarySigma(n) is divisible by UnitaryPhi(n)*n.
A129650	Largest order of a permutation of n elements with exactly 5 cycles. Also the largest LCM of a 5-partition of n.
A181312	Highly abundant numbers n whose largest prime factor is greater than log(n).
A181504	A000272(n+1) - A000951(n), n >= 6. Number of forests of rooted labeled trees with n nodes and height >= 5.