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# User:Peter Luschny/MyFabInt

From OeisWiki

## 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. |