75 (number)

75 (seventy-five) is the natural number following 74 and preceding 76.

In mathematics

75 is:

• the fourth ordered Bell number, and counts the number of weak orderings on a set of four items.^[1]
• the sum of the first five pentagonal numbers, and therefore a pentagonal pyramidal number.^[2]
• an enneagonal number.^[3]
• a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 7, 5, 12, 17, 29, 46, 75...^[4]
• a self number because there is no integer that added up to its own digits adds up to 75.^[5]
• a palindromic number in bases 14 (55₁₄) and 24 (33₂₄).
• a Harshad number in bases 3, 5, 6, 8, 11, 13, 15 and 16.

Excluding the infinite sets, there are 75 uniform polyhedra (or 76 if edges are allowed to coincide).

In other fields

Seventy-five is:

• The atomic number of rhenium.
• The age limit for Canadian senators.^[6]
• A common name for the Canon de 75 modèle 1897, a French World War 1 gun.
• The departement number of the city of Paris.

References

1. ↑ "Sloane's A000670 : Fubini numbers: number of preferential arrangements of n labeled elements; or number of weak orders on n labeled elements; or number of ordered partitions of [n]". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29. 
2. ↑ "Sloane's A002411 : Pentagonal pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29. 
3. ↑ "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29. 
4. ↑ "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29. 
5. ↑ "Sloane's A003052 : Self numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29. 
6. ↑ “Who are our senators and what do they do?”, Parliament of Canada, retrieved 2014-02-02.