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75 (number)

FieldValue
number75
divisor1, 3, 5, 15, 25, 75

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

TOC

In mathematics

75 is a self number because there is no integer that added up to its own digits adds up to 75. It is the sum of the first five pentagonal numbers, and therefore a pentagonal pyramidal number, as well as a nonagonal number.

It is also the fourth ordered Bell number, and a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 7, 5, 12, 17, 29, 46, 75...

75 is the count of the number of weak orderings on a set of four items.

Excluding the infinite sets, there are 75 uniform polyhedra in the third dimension, which incorporate star polyhedra as well. Inclusive of 7 families of prisms and antiprisms, there are also 75 uniform compound polyhedra.

References

References

  1. {{Cite OEIS. A003052
  2. {{Cite OEIS. A001106
  3. {{Cite OEIS. A002411
  4. {{Cite OEIS. A007629
  5. {{Cite OEIS. A000670
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