147 (number)

147 is the fourth centered icosahedral number. These are a class of figurate numbers that represent points in the shape of a regular icosahedron or alternatively points in the shape of a cuboctahedron, and are magic numbers for the face-centered cubic lattice.^[1] Separately, it is also a magic number for the diamond cubic.^[2]

It is also the fourth Apéry number ${\displaystyle a_{3}}$ following 19, where^[3] $${\displaystyle a_{n}=\sum _{k=0}^{n}{\binom {n}{k}}^{2}{\binom {n+k}{k}},}$$

with 147 the composite index of the nineteenth triangle number, 190.^[4][5]

There are 147 different ways of representing one as a sum of unit fractions with five terms, allowing repeated fractions,^[6] and 147 different self-avoiding polygonal chains of length six using horizontal and vertical segments of the integer lattice.^[7]

• 147 (disambiguation)